THE PRACTICAL TEACHER. 



THE 



PRACTICAL TEACHER 



OR 



FAMILIAR EXPLANATIONS & ILLUSTRATIONS 



THE MODUS OPERANDI 



OF THE 



SOHOOXj 3FL003VE. 



BY E. LAMBORN. 



LANCASTER : 

PUBLISHED BY MURRAY & STOEK. 

1855. 



.Li 



Entered according to Act of Congress, in the year 1855, 
BY MURRAY & STOEK, 

In the Clerk's Office of the Eastern District of Pennsylvania. 



PRINTER BV 

WM. B. WILEY, 

LANCASTER. 



TO 

II ON. T II O . II . BURROWES, 

ONE OF THE EARLIEST AXD 

FIRMEST SUPPORTERS 

OF THE 

COMMON SCHOOLS 

OF 

PENNSYLVANIA, 

THIS WORK IS RESPECTFULLY DEDICATED 

BY THE AUTHOR. 



CONTENTS 



Preface, 
Chapter 



i. How to Teach, .... 
n. The Teaching of Spelling, Reading, and the 

Alphabet, 
in. The Teaching of Grammar, 
iv. The Teaching of Arithmetic, 
v. The Teaching of Geography, 
vi. The Teaching of Geometry and Algebra, 
vii. How to Raise your Salaries, 
viii. Miscellaneous, .... 



Page 5 



19 
33 

54 

87 

94 

101 

105 



PREFACE, 



As teaching is about to become a distinct profession in our good old 
State of Pennsylvania, and a higher standard of professional attainments 
beginning to be demanded ; it is thought that a selection of educational 
precepts from the experience of practical Teachers, making a manual of 
practical directions, will be useful to Teachers generally, and especially to 
the young and inexperienced. 

The writings of Page, Mann and others, have, with the different Edu- 
cational Journals, done much to assist the School Teacher: and the conse- 
quence is — a general improvement in our schools. 

The race of sour, formal, bookish, pouring in School-masters is passing 
away ; and professional Teachers, endeavoring to assist the " young idea 
to shoot," are taking their place. 

But the wants of the practical Teacher of the Common School, 
seem to demand a work, which, while it is relieved of the superabundant 
matter, contains the practical part of the " Teacher's Library" and other 
educational works : together with the experience of many of our Com- 
mon School Teachers. 

He who has read Page, Northend, Mann, and others, has been profit- 
ed thereby. He who is a regular reader of an Educational Journal, is a 
better Teacher than he who is not. 

But the wants of the times, demand something more specific. 

Of what avail are the lofty harangues of Bishop Potter to him who 
cannot teach a child his A B C ? Normal Schools are the wants of the 
present age. Teachers' Institutes, which are springing up over the State, 
supply, in a degree, their place. They furnish Teachers, not only with 



6 PREFACE. 

general rules for teaching, but special directions, for the teaching of dif- 
ferent branches. 

This work is intended, in some degree, to supply their place. It will 
consist of a compendium of selections from the best Educational Journals 
and other works ; suggestions of practical Teachers, prepared by them 
expressly for this work, collected from their writings, their sayings at 
Teachers' Institutes, &c. 

It is an undeniable fact, that with all the valuable qualities necessary for 
the Teacher, described by Page, and others, he who knows not the quickest 
method of teaching the primary branches of the school-room, must, in 
this practical age, fail as a successful Teacher. The people of this age are 
too practical to be satisfied with the " waking up of mind " alone. ABC 
must be taught ; and while we admit that the old "pouring in " process of 
teaching is radically wrong, and that the system of " developing the facul- 
ties " of the child, so beautifully portrayed by different authors, should be 
the primary object of the Teacher, — we, as practical Teachers, need some- 
thing more. 

In accordance, therefore, with these views, the compiler, while keeping 
in view the "developing of the faculties" the "waking up" of mind, as the 
principal object of the Teacher, has selected, in addition thereto, from the 
experience of practical Teachers, the practical application of this theory in 
the teaching of A B 0, reading, writing, arithmetic, &c, &c, by modes, 
in their experience, the shortest and best. 

E. Lamborn. 
West Lampeter, Lancaster co., Jan. 1st, 1855. 



CHAPTER I. 

HOW TO TEACH. 
" To teach a child his A, B, C, is not to educate him." — Frs. Wayland. 

The first requisite for a successful Teacher is to love 
teaching. He who does not love teaching is not fit for it. — 
It has been remarked, that " he who can be lonesome with 
children, should leave the school room." It is equally neces- 
sary to make the school room, and all connected with it, inter- 
esting to the pupil. 

A Teacher of Lancaster county, writes as follows in the 
Pennsylvania School Journal: — "Kindness mixed with dig- 
nity of character, commands respect, and will contribute more 
to the enforcement of obedience than all the torture ever re- 
sorted to in the school room. Kindness begets love; and 
love is the strongest passion of the human heart. Armed 
with the powerful weapon of kindness, the Teacher's control 
is almost infinite." 

" Be kind', yet firm," says a celebrated Educationist. 

Having gained the confidence of both parents and pupils, 
(Avhich can be done most effectually at the fireside of the pa- 
rent,*) let there be " a good correspondence between master 
and pupil." Let your government be kind, but parental. — 
Make but few rules. A parent makes but few rules for the 
government of his family. 

Mr. Page says : " The main business in school is instruction 
and not government." 

Let the Teacher govern himself. A noisy Teacher makes a 

* Visit parents frequently. 



8 HOW TO TEACH. 

noisy school. Keep your pupils employed. Let industry be 
your watchword, and you will have order. Not that a child 
should be kept like a slave, with his eyes fixed mechanically 
on his book, " controlled in every look and action by the as- 
pect of authority, and his whole nature put under a discipline 
of repressions and restraint," but be kept at useful and phas- 
ing employment. 

" Variety is the spice of life" ; and with children, it can be 
made to afford a spice more exciting than even their accus- 
tomed play* " He is the successful Teacher," says Page, 
" who can excite and maintain the necessary interest."! As said 
in a succeeding chapter, the order of exercises must depend 
upon circumstances. A Teacher who understands his profes- 
sion, can regulate his own school. Page says, in his Theory and 
Practice of Teaching : " The circumstances of schools will be 
found to vary so widely, that no model, however perfect in 
itself, would answer for all. The Teacher must exercise his 
own ingenuity and judgment, to meet his own wants." 

But first, make your school house and grounds agreeable, 
pleasing and attractive ; and the task of making the studies 
within attractive, will be more easy4 We extract the follow- 
ing remarks from an article in the Pa. School Journal, by the 
lamented D. S. Kieffeb, of Lancaster county : 

" Four years ago, I commenced teaching in what is called 
the ' Sand-stone School-house,' in Strasburg Township — a de- 
solate, uninviting, prison-looking tenement, with nothing to 
protect it from the heat of summer, or the cold of winter. I 
proposed to the children, the improvement of our house and 

* Health, however, demands physical exercise. Pupils should not only 
be permitted to exercise, but encouraged. 

f Drawing and Music are exercises which will interest the dullest pu- 
pils, and which the whole school can take part in. Drawing may be done 
on the blackboard, slate, paper, or even on the floor. Any Teacher can 
draw a rough picture of a house, a tree or some familiar object, which 
the pupil will endeavor to imitate. Think not the time thus spent, lost. 

% I once taught in an old, dark school-house, which we were accustomed 
to leave every pleasant day and meet in an adjoining wood. 



HOW TO TEACH. 9 

grounds by subscription. The proposal was acceded to with 
alacrity, and being seconded by the parents, was soon put 
into execution. Our grounds were enclosed by a neat fence, 
the house was whitewashed, inside and outside, and things be- 
gan to assume a better appearance. 

" I then proposed that our enclosure should be converted 
into a flower garden. The ground was prepared, and every 
boy and girl brought some kind of tree or bush to be planted, 
each to own and cultivate what he or she brought. 

"In season, the fences are festooned with vines, and the 
paths bordered with flowers, which grow as vigorously, smell 
as fragrant, look as tasteful, and are preserved as carefully as 
though planted anywhere else than in the yard of a district 
school. 

" To one who has not had similar experience, it would be 
difficult to imagine the delightful interest manifested by the 
children in these simple auxiliaries to their enjoyment. 

" While these exterior arrangements were going forward, 
the interior was being furnished with blackboards, maps, 
charts, globes, thermometer, clock, library, &c, to facilitate 
learning." 

Let everything connected with the school room be calcu- 
lated to "inspire the mind with activity and delight." "Let 
everything be conducive to health and happiness : and pro- 
motive of moral, intellectual, and physical comfort." But, 
above all, let the pupils play: play in the open air: for upon 
it depend much of the " health, cheerfulness and tranquility' 
of the school room. 

The Popular Educator contains the following remarks : — 
" A child who has had the advantage of as much bodily ex- 
ercise as possible in spacious gardens and fields, until he has 
reached his seventh year, even if he should not then know a 
single letter, will soon overtake those who have their heads 
crammed with book information at an earlier period ; and not 
only overtake them, but outstrip them. And why ? Be- 
cause his mind is in a healthy state, as well as his body. All 



10 HOW TO TEACH. 

judicious instructors of youth are well aware that it will not 
do to exert the mind too much. What, for instance, does 
Humel say, whose ' Piano-forte school ' is one of the ablest 
productions that ever came under the notice of a musician ? 
He intimates that a very young pupil of delicate organization, 
and possessing a fine ear, must not be confined to the instru- 
ment more than four hours a day. 

"Who that has ever given the matter a thought, can ima- 
gine, for a moment, that the delicate and marvellous mind of 
Shakspeare, would have been developed in the way that it 
has been, if he had at an early age, been crammed with Latin, 
Greek and Algebra. 

"Every parent and teacher should be careful not to tax the 
time and application of the child beyond his strength. The 
pupil has an imperative claim to rest, and recreation, and 
amusement. To deny the play-ground, with its many games, 
and sports, and leaps, and loud-rising laugh, is to retard the 
progress of the mind. Much precious time is literally wasted 
in cramming the memory with words and phrases, which bar 
the admission of thought, and render application irksome. A 
mere effort of memory, is not the attainment of knowledge ; 
and words, instead of ideas and facts, make up but a poor ca- 
pital with which the future man is to carry on the intercourse 
and pursuits of life." 

" To teach successfully, the Teacher should be educated in 
his profession." He should understand the art of teaching. 

Francis Wayland says : " If there be any such art, as 
the art of teaching, we ask how it comes to pass that a man 
shall be considered fully qualified to exercise it without a 
day's practice, when a similar attempt in any other art would 
expose him to ridicule." 

We will now come to the subject denoted at the head of 
this Chapter : and, in our opinion, more depends upon the 
manner of teaching than the order of exercises. 

" It is desirable," says F. Wayland, " that the pupil should 
be taught thoroughly ; that is, that he should have as exact 



HOW TO TEACH. 11 

and definite a knowledge as possible of the law and of its re- 
lations. It is desirable that he be taught permanently: that is, 
that the truth communicated, be so associated with his other 
knowledge, that the lapse of time will not easily erase it from 
his memory. It is important also, in this practical age, that 
no more time be consumed in the process than is absolutely necessa- 
ry. He who occupies two years in teaching what might as 
well be taught in one year, does his pupil a great injury. He 
not only abstracts from the pupil's acquisition, that year's im- 
provement, but all the knowledge which would have been the 
fruit of it for the remainder of his life." 

How often have we seen pupils, nearly arrived at manhood, 
who, after having gone to school every winter since they were 
old enough to attend school, and during their earlier years, 
both summer and winter, had learned nothing but to be mis- 
erable scholars, who neither knew how to spell, read, write 
nor cast accounts ? 

Now, the quickest way to do anything is to do it right. — 
Better spend the whole time in teaching the elements, than to 
advance the pupil before he is acquainted with them ; for with- 
out them, he can effectually learn nothing ; and no time can 
be gained by attempting to pass on without them. If he can- 
not learn the elements he can learn nothing else. But have 
patience. " Patience and perseverance work miracles." When 
at length he has mastered the elements, he goes ahead as if b} T 
magic: and the time apparently lost is repaid a hundred 
fold. 

Let reviews be frequent. " What is understood to-day, 
may with pleasure be reviewed to-morrow." But keep in 
view that " to teach a child his A, B, C, is not to educate 
him." 

James G. Carter says : " In vain you put into the head of 
the child the elements of all the sciences ; in vain will you 
natter yourselves that you have made him understand them. 
If there has been no endeavor to develope his faculties by 
continual, yet moderate exercise suited to the weak state of 



12 HOW TO TEACH. 

the organs, if no care has been taken to preserve their just 
balance, so that no one may be greatly improved at the ex- 
pense of the rest, your child will have neither genius nor ca- 
pacity ; he will not think for himself, he will judge only after 
others ; he will have neither taste, nor intelligence, nor nice 
apprehension ; he will be fit for nothing great nor profound ; 
always superficial ; learned, perhaps in appearance, but never 
original, and perpetually embarrassed whenever he is put out 
of the beaten track ; he will live only by his memory, which 
has been diligently cultivated ; and all his other facilities will 
remain, as it were, extinct or torpid." 

Better that the pupil should leave school, a thinking being 
with his faculties fully developed, than to be profoundly 
skilled in the depths of learning, and be "a learned 
dunce." In the language of Page, " let the pupil's mind be 
waked wp." Create an interest in his studies. This is the grand 
point. He who can do this, can make his pupils study. But 
how, some may ask, is this interest to be excited ? Let the 
Teacher himself be interested, and he will soon find that his 
pupils are interested. As the Teacher who governs himself, 
finds no difficulty in governing his school, which, as it were, 
governs itself, so if the Teacher be not idle, neither will be his 
pupils. 

Much has been said by writers on education respecting the 
order of exercises, classification of pupils, &c, &c, all very 
good. I, however, intend to dwell more particularly upon 
the methods of teaching the various branches taught in the 
school room, leaving the classification and arrangement of the 
school to the judgment of the Teacher. 

Make a pupil understand what he is doing. A child will 
not even play without a motive. I once heard of a man in 
search of work, who was given the task of turning the empty 
grindstone : and though well paid, he soon tired, and gave up 
his job. So with the pupil who conns lessons without mean- 
ing : and who knows not what he is doing. He should be 



HOW TO TEACH. 13 

treated as a reasonable being, and be required to do nothing 
without a motive, which he understands. 

Mr. Carter " once knew a child, who, the first day he en- 
tered the school, was assigned the first seven letters of the al- 
phabet, and sent to his seat to learn his lesson. Do you think 
it strange," he says, " that he found it difficult to confine his 
attention to his book ?" 

To learn, a child must love his studies, and to love them, 
he must understand them ; and if he understands them, it is 
not a difficult task to make him love them. If he becomes 
wearied, change the exercise. Let him play, or sing, or in 
some way relieve the monotony : and he will renew his study 
with fresh vigor. 

F. J. Grund says: " Children the most unlike are often put 
together in the same class, and have to learn, each day, a fixed 
portion of one science or another, and the test of their ac- 
quirements is a verbal recitation from a book. The memory 
is charged with the crudest and most heterogeneous concep- 
tions, without allowing the mind the least respite, to assort 
and adjust them,much less the time which it need to reflect upon 
them. Thus, from the first moment the boy goes to school, un- 
til the young man leaves college, he is harrassed and haunted 
with studies for which he has no spirit or inclination : and it 
it is a wonder if his mental powers are not prostrated or de- 
stroyed." 

" The belief is yet too common among parents," says the 
same author, " that education consists in learning and apply- 
ing certain dogmatical rules, without caring for their being 
understood." Even the most enlightened seem pleased that their 
children "are through the book." The more branches that are 
crammed into the mind, or pretended to be, the better the pa- 
rents are pleased. The practical teacher is, therefore, necessita- 
ted, in some measure, to compromise his principles ; and while 
he takes care to make the child a thinking being, to awaken his 
faculties, "enable the pupil to acquire knowledge by his own ex- 
ertions," he must make the parent believe that his child has swal- 



14 HOW TO TEACH. 

lowed the book. This confidence must be gained. I once 
knew a Teacher who, during the first week of his school, 
heard his reading classes six lessons in the morning, and six 
in the afternoon of every day in the week. I know not how 
his plan succeeded, but if he thereby gained the confidence 
of his patrons, without which he could not teach his pupils, 
he was excusable for a week's loss to his school. 

In fine, the Teacher who would succeed, must enter the 
school house with the determination to instruct the pupils en- 
trusted to his care ; and with this, he need not trouble him- 
self with systems of government, rules of order, or forms of 
exercises. As to government, it will take care of itself. He 
who is zealous for the improvement of his scholars, as a pa- 
rent is for his children ; he whose intercourse with them is as 
free and unreserved, as a father's with his children, needs no 
rules : he will know nothing of disorder : his school will be 
governed, for it will govern itself: and he whose school is not 
thus governed, will experience the difficulty experienced by 
most Teachers, of " governing too much." He who governs 
least, mostly governs best ; while multitudes of rules, are 
mostly promotives of disorder. School government, then, be- 
ing only a " good correspondence between master and schol- 
ars," the modes of imparting a knowledge of the various 
branches of education, {the modus operandi' of the school-room) 
seems to be the only requisite to the faithful Tteacher. That a 
Teacher may be faithful to his trust, and be profoundly learn- 
ed in the sciences which he is to teach, yet deficient in the 
best methods of imparting that learning to his pupils, is an 
admitted truth. And, although a skilful teacher will mostly 
arrive at correct conclusions, and adopt modes of imparting 
knowledge in his own school more successful than any learn- 
ed from others ; yet what Teacher has not been improved by 
the experience of others ? He who blindly adopts a mode, 
because it has been successful with another, will not succeed : 
yet he may from it derive something of lasting benefit to his 
school. Most successful Teachers although not blindly adopt- 



HOW TO TEACH. 15 

ing any mode of teaching, are yet familiar not only with the 
best works on education, but the modus operandi of their fel- 
low Teachers. What is more beneficial to the young Teacher 
than "mutual improvement" meetings of Teachers, where 
each gives his own experience of teaching, school-government, 
&c, or what more beneficial than mutual visitation of schools? 
Even from their faults we learn. 

Thus, then, while we re-assert that the successful Teacher 
will not blindly adopt any method untried, and that the me- 
thods obtained from a Teacher's own experience, are general- 
ly the most successful, yet he who is best acquainted with the 
modes of others, is generally himself most efficient. From 
the mass, he selects the best. We, therefore, in the succeed- 
ing chapters, will endeavor to describe, not only the experi- 
ence of a Teacher who thinks it no presumption to say, that 
he has been, in some degree, successful ; but methods of teach- 
ing the branches of a common school education practised by 
some of the best educators of the age : and sanctioned by the 
highest authority. One thing we insist on throughout, not 
to place too much dependance upon the arrangements of the 
books. " The best book on any science needs much aid from 
the instructor." 

" If a Teacher can do no more," says another Teacher, "than 
repeat the printed questions at the bottom of the text-book, 
and hear the ready-made answers, he had better quit the bu- 
siness." 

"I am of opinion," says Page, "that aptness to teach, like 
aptness to do anything else, is usually an acquired power, 
based upon a correct knowledge of what is to be done, and 
some accurate estimate of the fitness of the means used for 
the end." 

Again he asks : " How far shall I assist the pupil, and how 
far shall the pupil be required to assist himself?" The mode, 
as explained in the subsequent chapters, is to tell the pupil 
nothing directly, further than to make him fully understand 



1 6 HOW TO TEACH. 

what he is at ; but always have something to be done by the 
pupil himself. 

Mr. J. P. Wickersham, in vol. II, page 141, Pa. School 
Journal, says : " Make the subject intelligible to your pupils. 
Not only should the subject be made intelligible to the pupils, 
but it should be presented in such a form as to be attractive, 
and to secure attention. An anecdote or story is now and 
then appropriate ; and if a fact in the personal history of any 
member of the class can be introduced, or some occurrence in 
every-day life, or, which may have happened about the school 
room, can be made available (and no lesson need pass without 
some such allusion) it will never fail to secure attention. In 
Grammar, sentences can be given in which the names of some 
of the pupils may be embodied ; and in arithmetic, transactions 
in which they figure as parties ; and not unfrequently the 
careless and intractable may be made to work manfully by 
some such artifice. 

"In hearing a recitation, the Teacher should generally stand 
— always, if the class is large. It may look dignified to sit on 
a platform or behind a desk, and demurely doll out questions, 
but surely it is not the best way to interest pupils of any age. 
Let the Teacher stand in front of his class ; and his eyes, his 
countenance, his gestures, the very motions of his body, all 
speak, and assist in impressing what his tongue would utter. 
The effect of an oration would be greatly impaired, if the ora- 
tor delivered it in a sitting posture ; and so the instructions 
of the Teacher. 

" Questions as to the kind of answers required, may be ask- 
ed in two ways ; first, in detail, requiring but a single sen. 
tence, or a few sentences, to embrace the answer ; second, by 
subjects embodying many details in one general question. — 
The former method is probably the most searching, while the 
latter inculcates broader views of the study, and cultivates to 
a greater extent the powers of generalization and expression ; 
and both, doubtless, should be practised. * * 

" The written method may be divided into the blackboard 



HOW TO TEACH. 17 

method and the slate method. The oral may be divided into 
the turn-about method, the selecting-out method, the uplift- 
ed hand method, and the concert method. * * * 

" In the selecting-out method, the Teacher gives out the ques- 
tion to the whole class, and after allowing a little time to 
think, names the answer. By this method, the attention of 
the whole class is enlisted. All must think at the question, 
and this alone is worth something. * * * * 

" The uplifted hand method is a modification of the selecting- 
out method, and differs from it only in this, that when the 
question is put, all that think they can give the correct an- 
swer, raise their hands, and from these, the Teacher selects 
the answerer. It makes a lively recitation, and enables the 
Teacher to tell, if not deceived, how many are able to an- 
swer." 

Sometimes the Teacher finds it difficult to fix the pupil's 
attention to any study. The pupil may be dull in mathema- 
tics and grammar, he may feel no interest in them, which the 
Teacher strives in vain to excite. But he has not touched the 
right chord. There is a chord to every person's heart which 
will vibrate, when touched : and which will arouse other emo- 
tions which have lain dormant. Cause an interest in one sub- 
ject, and it will lend an interest to others. I once had a pu- 
pil who appeared to be insensible to everything connected 
with the school room, until near the close of the session, 
when the preparation for an exhibition aroused his energy, and, 
as his parents declared, "he learned more in three weeks, not 
only in reading, but in other studies, than he had during the 
previous part of the session." His interest in a portion of the 
school exercises, was excited, which was easily transferred to 
the others. Independent of school exhibitions, which I do 
not recommend, the Teacher can find something to interest the 
pupil ; drawing, music or even hearing the lessons of the 
smaller pupil, something to make him think he is good for 
something. Let him know that he is good for something, and you 
have something to stand on, to work the lever of instruction. 



18 HOW TO TEACH. 

Emulation may, in many cases, excite an interest in study : 
but it does not always succeed. A judicious Teacher will 
guard well this principle. That it works well in a class of 
pupils, with attainments nearly equal, we have experienced : 
but who has not seen in a class where the few surpassed the 
others, that the others " fall into hopeless indifference ? "Who 
has not seen in a class, where the strife was for head, all but 
two or three quite as well satisfied with being at the foot ?" — 
Much more might be said respecting the modes of teaching, 
and the waking up of miiid* but leaving this subject so ably dis- 
cussed by others, we pass on to the methods of teaching the 
different branches. Before closing this chapter, I would, how- 
ever, impress upon the Teacher, the necessity, in the govern- 
ing of his school, of being firm. "What mode soever you 
adopt, let your word be law. Be mild, yet firm. A school can- 
not be a republic. The Teacher must be the monarch, from 
whose will there is no appeal. 

* See Page's admirable chapter on " Waking up mind." 



CHAPTER II. 

THE TEACHING OF SPELLING, READING, AND THE ALPHABET. 

To teach spelling has been considered an arduous task ; a 
labor of many months ; and even years. To obtain a thorough 
knowledge of orthography and ortheopy, is yet a labor of 
years, and will be until a phonetic system is introduced ; but 
to teach a child to be a tolerable speller, i, e. to be able to spell 
and pronounce with ease and facility, the ordinary words of 
our language, and to read with fluency in the shortest time, 
and with the most ease to Teacher and scholar, is the province 
of the Common School Teacher : and this is what we propose 
to treat of in this chapter. To be able to write without mis- 
spelling ordinary words, and to read ordinary reading, are the 
primary studies of the School-room. G. F. Thayer, says : 

" Numerous as are the innovations in, or (to adopt a more 
acceptable term) new methods of teaching the various branch- 
es of education at the present day, I hold those only to be im- 
provements, which present the subject in a more practical form ; 
which will require the least change from the school-method 
to that to be pursued in the business of life. 

" If, then, we look for a moment at the common mode of 
teaching spelling, viz : to assign one or more columns of 
words, in a spelling book, to be committed to memory, and ut- 
tered by the voice, letter by letter ; we see one entirely at va- 
riance with practical instruction, tedious to the pupil, expen- 
sive in time to the instructor, and never to be used in after life ; 
of course, one that needs reformation, and in relation to which 
2 



20 THE TEACHING OF SPELLING, 

almost any change would be an improvement." Again he 
says : 

" The practice once so common of assigning lessons in spell- 
ing and defining from the columns of a dictionary is one of 
the most stupid and useless , exercises ever introduced into a 
school." 

Every Teacher who has practiced this mode, can bear testi- 
mony that the pupils thus taught, do not remember the defi- 
nitions ; and as the same author says ; " even if they could be 
remembered they would be of doubtful utility ; for, as the 
right application of a definition must depend entirely on the 
situation of the word to be explained, and the office it per- 
forms in a sentence, the repeating of half a score of mean- 
ings — as obscure, perhaps, as the word itself — conveys no defi- 
nite thought, and serves rather to darken, than illuminate the 
mind." 

How often have the feelings of the Teacher been mortified 
by the practical spelling of the best spellers of his school. — 
How often do we see a boy who can spell {off the book) every 
word in the spelling book, unable to write a letter -without 
mis-spelling half the words ? 

Of this important branch of education, Wm. Eussel lays 
down the following primary rules :* 

" Every exertion should be made to render the school-room, 
and the school furniture, conducive to health and comfort. 

" The school exercises should be often varied, and the atti- 
tude of the children, frequently changed. 

"Motion at short intervals, should be a part of regular 
school exercises. 

" The school should be ruled by management, rather than 
government. 

" A mild, affectionate and judicious treatment of individu- 
als should be substituted for general laws and penalties. 

* These remarks more properly belong to Chapter 1st, but as they have 
particular reference to "primary schools" we introduce them in this Chapter. 



READING AND THE ALPHABET. 21 

"Conscience, judgment, affection, sympathy, arid not fear, 
should be employed, as means of moral influence. 

" Lessons should be very short, as well as simple ; and strict- 
ly adapted to the powers and capacities of the pupils : and 
nothing taught to be understood by and by." 

I repeat, let the children play. Nature demands it : health 
demands it. You can teach more in the interim, than in the 
whole time. Their minds will be invigorated ; they will learn 
faster ; and finding that they learn, they will love learning, and 
learn faster still. 

I will now give a few gleanings from my own experience ; 
and also from others who have given their experience to the 
world, in the teaching of this most important branch of educa- 
tion : but it is to be regretted that so few Teachers have 
thought this subject worthy of much notice. 

The words of the reading lessons, which contain the most 
common words, and, therefore, the most useful,* are among 
the child's first spelling lessons. As to the primary books, 
there is so great a variety, that it is next to impossible to 
make a choice, but the Teacher cannot go amiss, if he be care- 
ful to select easy sentences, and pleasing to the pupil. I never 
found any sentences more pleasing to the pupil than the 
following from Bonsai's edition of Comly's spelling book : 

" We had a red cow and a fat pig." 

"The boy cut his lip on the ice." 

As to the lines of spelling composed of long difficult words, 
they may be left until the pupil can spell, read and write, with 
tolerable facility the most common, simple, and consequently 
most useful words. As the pupil advances, the principles of 
reading should be attended to. The pupil should never be 
allowed to sing or drawl his words ; and until he can put his 
words together correctly and understandingly, which is read- 
ing, let him continue to spell mentally : — which is not read- 

* Professor Thomson, of Pittsburg, once remarked, that it would be 
better to burn the spelling books than to use them merely to teach the 
child words, instead of ideas. 



22 THE TEACHING OF SPELLING, 

ing .* One point must be carefully observed, and that is a 
clear, full and distinct articulation. As Dr. Austin says, 
" Every "word should be delivered from the lips as beautiful 
coins newly issued from the mint, deeply and accurately im- 
pressed, neatly struck by the proper organs, distinct, in due 
succession, and of due weight." As Dr. Comstock says : 
" Without good articulation it is impossible to be a correct 
reader." 

As soon as the pupil can write, put him to writing his own 
composition; which will, of course, be composed of easy 
words. Writing by dictation, is a valuable exercise, one pu. 
pil correcting the errors of the others. Such exercises as 

" What can ail our friend Thomas." 

"He has drank too much ale." 

" The air was pleasant." 

" He was sole heir to the property," 
from Northend's " Dictation Exercises," are very useful. — 
The pupil may write them on a slate : then copy them off on 
paper, and carry them home at night for correction by the aid 
of the dictionary : to be returned next morning for the Teach- 
er's inspection. This exercise teaches them to spell, to write, 
and to think. This is to improve his knowledge of spelling. 
The idea that a child must not be put to reading until he is a 
good speller, is now nearly abandoned by Teachers. 

f The whole art of teaching reading, is to teach the child to 
be natural. From wrong training in the early studies many 
children have imbibed a " school boy drawl " ; some a habit of 
cutting off or swallowing many of their words," &c, &c. These 
errors may be corrected by the Teacher's example. In reading, 

* The mere calling of words is not reading. It may be called " mental 
spelling." This may be practiced in various modes. " Word about " (as 
the pupil calls it) or the speaking singly, by each pupil, a word in turn, 
is a very efficient mode. This is different from spelling aloud the reading 
lessons which is also very effective in teaching words. I was once asked 
by a visitor, how I prevented my pupils from learning to drawl, when 
practicing this tvord. about exercise ? I answered, that as no principle of 
reading is involved in it, but merely mental spelling or word making, I re- 
quire them to pronounce every word in the falling inflection. 

t Pa. School Journal. 



READING AND THE ALPHABET. 23 

much is learned by imitation. I have always found that a 
child taught to read his school books correctly, without rule, 
by imitation alone, will read correctly in other books. True, 
to read well, he must understand his subject ; although, all 
who understand are not good readers. But to be natural in 
his reading, i. e. to use the correct tones and inflections of the 
voice, will teach him to understand what he reads : and this 
can be learned by imitation. I never saw a child whose read- 
ing was natural, no matter by what process taught, that did 
not understand what he read, unless it was above his compre- 
hension. 

The voice of the Teacher is the best thing, in my experi- 
ence, to teach a correct style. A Teacher who does not read 
much, and often, to his pupils, is not often successful. For 
how is he to teach the intonations of the voice, inflections, 
emphasis, &c, without that which reaches the pupil's ears? — 
Of what use is it, to tell a child that A has four sounds, E 
two sounds, without teaching him what those sounds are ? — 
No sound can be learned but by imitation. Can a Teacher 
teach the sounds of music, without giving those sounds to the 
pupil's ear ? No. Neither can he the sounds of the reading 
voice. Where is there a more beautiful and appropriate col- 
lection of rules for the reader, than in Murray's "English 
Header " ? Yet I have never seen the pupil who could prac- 
tice them, without their practical illustration by the Teacher's 
voice. The pupil must be able to speak, distinctly, every ele- 
mentary sound of the language 

* "He should be required to pronounce, clearly and dis- 
tly, A ! , A 2 , A 3 , A 4 , and every other elementary sound : and 
in reading, to distinctly enunciate every sound of every word. 

" The elements should be sounded by the pupils, daily ; and 
in every variety of pitch and force, to strengthen the vocal 
organs, and to improve the pupil in the intonations of voice. 
Even the postures of mouth should be attended to." 

* Report of Committee of State Association. 



24 THE TEACHING OF SPELLING, 

Correct tones, inflections, modulation, emphasis, &c. are bet- 
ter taught bj the Teacher's voice than by any rules. 

My* method of securing attention, is to commence at any 
part of the class, without regard to " head " or " foot." The 
pupil reads until the Teacher says " next ;" when the next in 
turn commences at the exact word, (or part of a word) where 
the former ceased, or forfeits his place in the class. One word 
from the exact place in the book, which may be lost by one 
look from the lesson, detects the careless scholar. If this fails to 
secure a thorough attention (as it sometimes does, when the 
class is large) the Teacher, instead of calling " next " — calls 
"John," "James," "Susan," or by numbers, promiscuously, 
without regard to his or her position in the class : each one 
knowing neither when nor where he may be called upon to 
read. If this fails, the Teacher keeps a watchful eye on the 
class: and the instant he sees an eye wander from the book, 
the name is called. If it is necessary (as it sometimes happens 
to be) to attend to another class, during this exercise, the read- 
ers cannot abate their attention : each one not knowing when 
he may be called upon, although but one may continue to 
read during the time the Teacher is engaged. Sometimes a 
touch on the shoulder with the finger is a signal to the reader 
to stop, and a similar tap, a sign for another to proceed. This 
is the most effectual method of securing the attention of the 
habitually inattentive ; as it deprives any one of an opportu- 
nity of catching the last word that is sometimes inadvertently 
dropped by the reader after the call of another name. 

The advantages of these methods, are : 

First, It secures a constant attention to every word ; as an 
omission for a single instant to look at the lesson, is liable to 
detection. True, a system of what is called, in the school-room 
vocabulary " trapping," may have the same effect with some : 
for others, nothing is wanting but their own ambition : but 
all Teachers know that such are "few and far between;" and 

* Pa. School Journal. 



READING AND THE ALPHABET. 25 

that for those not well acquainted with words, nothing but the 
most rigid exactness in requiring their attention, and their 
whole attention to the lesson, can be made available. And 
how is this attention to be secured ? The diligent pupil, as 
before said, needs not such discipline. But, all Teachers know 
that many pupils, even in the higher classes, though familiar 
with words, are very inattentive to their reading lessons, trust- 
ing to that familiarity to enable them under ordinary circum- 
stances, to be ready in turn, to read their part. But, the sys- 
tem described, compels even the best to be watchful : as he 
may, in an unlooked-for moment, be called upon; and, one 
glance from the book, may cost him his place. On the con- 
trary, in reading by verses, paragraphs, or even indefinite por- 
tions in regular order, he looks not at his book until his time 
arrives ; but with finger on his place, he stands, idly awaiting 
that time, without seeing a word read by the others. When, 
at length, a dozen or more have drawled through their parts, 
he reads his part, counts the verses ahead, and again awaits 
his turn. I do not say that, with the watchful Teacher, this 
must be the result even of the latter mode, but it is certain 
that with the former, the pupil cannot, under any circum- 
stances, neglect the lesson with impunity. 

This method is also practiced in spelling. I sometimes stop 
the pupil before the word is finished, giving the signal to an. 
other to proceed from where the former ceased : precisely, 
even to the letter. 

True, this method is tiresome to both Teacher and pupil ; 
and probably keeps the mental powers of the child too much 
on the rack of exertion ; but, as a recompense for their atten- 
tion, (instead of being sent to their seats, there to sit in un- 
meaning stillness, with vacant eyes fixed upon their books,) 
they are given the largest liberty, short of disturbing the 
school, when the recitation is finished. 

My* mode of teaching the alphabet, is to teach it in con- 

* Pennsylvania School Journal. 



26 THE TEACHING OF SPELLING. 

nexion with words. I sometimes commence it with four 
or five easy syllables as ab-di-ca-tion, or easy monosyllables, 
as dog, cat, pig, &c, and teach thoroughly, every letter 
in these words: also the pronunciation of every word 
and every syllable. Thus learning the letters as he learns 
to spell, the child soon learns not only his letters, but 
many words in as short a time as with a previous knowledge 
of the alphabet : thus saving the time usually spent in teach- 
ing it. 

This has been my plan for years ; and it superceeds the use 
of the regular alphabet ; as words and letters are taught in 
less time, and more easily (when taught together) than the 
alphabet alone. 

True, meddling parents sometimes object, and "wonder how 
the teacher is to lam the child to spell before he lams him his 
A, B, Cs — and persist in sending primers in spite of the 
Teacher's orders. But, mind them not : persevere, and you 
will come out right in the end. 

One of my pupils, a little boy, having been taught in this 
way, in spite of almost daily orders to put him at the begin- 
ning of the book, his papa concluded, as a last resort, to go 
to the school, and give the Teacher a lecture on teaching. But, 
thinking that he might as well first try his boy, and finding 
him good at the alphabet, he put him at b-a-ba's and so on to 
two syllables ; when he was content to indefinitely postpone 
his intended visit. This I afterwards learned from himself. — 
The next morning after this discovery by the parent, the lit- 
tle boy (who had also made the same discovery,) came to his 
Teacher, his eyes sparkling with joy, saying — "Mr. Lamborn, 
I can spell in b-a-ba, and nobody ever taught me." 

When the alphabet is sufficiently known, the pupil is trans- 
ferred to the second class in spelling : which is practiced in a 
manner similar to the mode of teaching reading, already de- 
scribed. Each pupil is required to spell until the signal to 
stop ; which may be at the end of one, two, or three, or more 
words, or in the middle of a word. Another then goes on, 



READING AND THE ALPHABET. 27 

commencing where the former left off (exactly at the very 
letter,) and so on promiscuously through the class. The 
backward pupils are thus given an opportunity of an extra 
portion of instruction : while all are compelled to be attentive 
or forfeit the place. Attentiveness thus becomes a "habit ; and 
whether the pupils spell promiscuously, or in regular class ro- 
tation, they are equally attentive. Not knowing when he may 
be called on, each pupil finds it necessary to be attentive un- 
der all circumstances. 

I find, in my experience, that a child accustomed to atten- 
tion in one class, is mostly attentive in others. But, fellow 
Teachers, perhaps the better mode would be to interest a child 
in his learning : better than to " hire, punish, or persuade, or 
even to excite emulation ;" yet to interest a child in the mere 
spelling of words, by any other mode than a spirit of emula- 
tion, seems to be attended with difficulty. 

I once had two boys who did not know a letter, entrusted 
to my care, to be taught for a stipulated sum, to read and write in 
a month. They were taught in the time. True, their knowl- 
edge was merely mechanical. Their writing was a mere 
scrawl of their names : nothing more. I give not this exam- 
ple as a correct mode of teaching, but of what may be done 
by a purely mechanical and forcing process. In this case, my 
system was beneficial ; for who will say that it was not bene- 
ficial to the poor boys ? Ay, it was. They were old enough 
to know that it was the only schooling they would ever re- 
ceive : and they improved the little all that had been given 
them. 

I wish to be understood that I consider the only advantage 
gained by putting a pupil at once to words of five syllables, 
is that he obtains a knowledge of the whole word in as short 
a time as the separate syllables alone ; as the pupil is required 
to pronounce each syllable clearly and distinctly. I do not 
contend for this mode : it is mine. I have succeeded with it. — 
Perhaps it would be better to put him to the reading lessons 
first : but I would never teach the alphabet unconnected with 



28 THE TEACHING OF SPELLING, 

words. By the mode I have described a pupil of ordinary 
talent, can be taught (including the letters) to read easy read- 
ing in four weeks. I however keep him at these spelling les- 
sons only until he has learned a few letters and acquired some 
idea of forming words : when I put him to words of easy 
reading lessons.* Either mode is better than the b-a-ba, b-l-a 
bla system : for with the same knowledge of these detached 
syllables, he has that of the whole word. 

Much has been said about educating the faculties, and in 
the last chapter, the views of several distinguished Teachers 
are given respecting the true method of educating a child, but 
to the practical Teacher in this practical age, a mode of teach- 
ing the child to spell and read as soon as possible seems to be 
the desideratum. " It is the dictate of common sense," says 
Mr. Page, "to take human nature as it is, and is likely to be 
' for some time to come. Human nature is far from being 
perfect ; and, I am sorry to say, that the parents of our child- 
ren, often exhibit it in no nattering light." 

f Although to educate the child's faculties, to make him a 
thinking being, to "wakezvp Ms mind/'' is doubtless the "more 
excellent way f yet the mode of doing it the way a child is 
taught to think, how to place the mental food within his reach, 
so as to render it most attractive, in short, the practical teach- 
ing of the "young idea," seems to be the difficulty, and one 
which the practical Teacher of the primary school, alone knows 
anything about. To interest a child in his play-things is not 
a difficult task. Neither is it difficult to interest him in the de- 
velopment of his own mind. 

" Delightful task," (says the Poet) "to rear the youthful mind." 

* An advantage of this mode is, that the pupil is more interested in 
learning to spell words which he understands, as dog, cow, pig, &c, and 
consequently learns both the letter and the orthography sooner than in 
other words. He may also be taught a few articles, verbs, &c, so as to 
make a sentence, as — " the dog, the pig, and the cow are fed " — when he 
may make a first attempt at reading. This is still more interesting to him, 
and adds a further impetus to his learning. 

t Pcnnsjdvania School Journal. 



READING AND THE ALPHABES. 29 

"Delightful task" too, to teach the higher branches: neither 
is it difficult to make them interesting to the student. 

But to make ABC interesting to the child appears to be 
a desideratum. It is that which is demanded : it is that which 
you have to do : and which it is your interest, Fellow Teach- 
ers, to learn to do in the shortest time, and with the most ease 
to yourself and pupils. 

I once taught a school, in which were too little boys ; one, a 
regular pupil, the child of a neighbor, and the other a voluntary 
pupil. The latter, when prevented from attending the school, 
cried to come ; and when there, none but the Teacher could re- 
move him without force. The former also cried to come to school 
on the first day ; but in a week, cried to stay at home. Why ? 
Because, as he said, " the long lessons tired him." The latter, 
a remarkably active, lively boy, continued to like the school, 
and so well that he would willingly sit in quietness during 
several hours each day, rather than leave the school. He is 
sometimes permitted to say a lesson. The former was a book 
drudge, the latter would have become a thinker. 

At different times during my teaching, I had two little girls 
given to my care. They commenced their studies, as the lit- 
tle boy, spoken of; and in two years, were better scholars 
(even book scholars) than any others ever taught by me in 
the same time. 

I throw out these facts as hints of the true principle of 
" training the young idea ;" as practical Teachers, we are ar- 
rested on the threshold by parents, who try their children by 
the book. 

Who has not heard the complaint, "My child has gone to 
school so long, and doesn't know his letters. 

We dare not often trust our reputation, and interest as 
Teachers, with our most liberal patrons. They judge, not by 
what the child knows but by the words he knows in the book. 
All that he knows besides his book knowledge, is attributed 
to his own natural talent : and the Teacher is the more liable 
to censure, for not teaching so promising a child. Better for 



30 THE TEACHING OF SPELLING, 

the reputation of the Teacher that he cramp every energy of 
the child, except that which is bent, from morning till night, 
over an unmeaning book lesson : for the dullness of the child, 
is not attributed to the Teacher, who rather receives additional 
praise for teaching one so unapt. 

But, even ABC can be made interesting, and taught 
without cramping the powers of the child. We need no forc- 
ing system, even in this most uninteresting of all studies. — 
Much better to let the child play three-fourths of the time ; 
he will learn more in the remaining fourth than in confine- 
ment for hours in succession, "enduring an irksome restraint," 
the whole time. The child should love his school ; ay, even 
his ABC. 

We should reject the forcing system, 

First, because it injures the child. 

Second, because it is the slowest way. 

Do not fear that you cannot make him interested in his 
first studies. He may even so love them, as to be necessary 
to curb him. 

The greatest punishment inflicted on the little girls men- 
tioned (besides sending them from the school-room) was to 
deprive them of their books. 

Now, with such an interest, could not the first studies 
spoken of, be taught in connexion with the training of the 
" young idea ?" If so, we have gained a new point in the sci- 
ence of education. The only danger seems to be, that by cre- 
ating too great an interest, we overtask his faculties and tax 
too much the mental powers of the child. 

But, be that as it may, we must satisfy the parents. The 
public mind is not ripe for throwing away the child's A, B, C. 
Those who acknowledge the theory, measure the Teacher's 
qualifications by a different rule. We know what our pa- 
trons expect of us : and we know that a Teacher who can 
teach a child to spell and to read (i. e. to say words) in the short- 
est time, will receive the best support: and we must meet the 



WRITING AND THE ALPHABET. 31 

emergency.* To do this with the least injury to the child 
mentally and physically, seems, therefore, to be the duty of 
the Teacher : and the mode described seems to have this pro. 
perty : always keeping in view — plenty of play ! plenty of 
physical exercise ! It is less irksome to the child, and less 
troublesome to the Teacher : and the pupil learns much more 
(even book learning) than by the confining method.f 

But, to proceed, Mr. Thayer says: "The pupil may be 
required to define such words from his reading lesson, as may 
be given to him, and subsequently to write them on a slate 
for a spelling lesson : if he be directed to write the meaning 
also, so much the better will it be for his progress in the lan- 
guage. The pupil may also be permitted to paraphrase his 
reading lesson, in his own language, according to his under- 
standing of it ; by which the Teacher can ascertain whether 
he had a correct idea of the subject, as well as individual 
words. The Teacher may thus lay the foundation of the pu- 
pil's style in composition. This exercise, will be found to be 
a very agreeable one to the pupil, who now may be permitted 
to use the dictionary. The Teacher may also mark in the 
reading lesson, such words as he deems most suitable and 
useful, and let the pupil search in his dictionary for such 
words as can be substituted for them, without changing the 
import of the lesson. This practice continued for a while, 
prepares the scholar for reading with unhesitating fluency." 

I have found much advantage to be derived from requiring 

* I have now in my mind's eye, a Teacher of the first class, {A, No. 1.) 
who, to use a common phrase of his patrons, "has the smartest set of 
scholars, but he can't make anything out of them." They are " smart." Ay, 
who made them "smart f" " Why, my little boy went to him six months, 
and didn't learn a letter." " Why do you keep him ?" suggested a friend. 
" Oh, the scholars like him so well," was the reply. 

" He didn't learn a letter ?" This is the kind of learning that is appre- 
ciated, and until the parents themselves are educated, is the kind we 
must learn to teach. 

t A lady once placed a little girl of five years old under my care, with a 
charge to not "push her too much, but let her play a good deal." By obey- 
ing her orders, the child learned the faster, — and the mother was not dis- 
pleased. 



32 THE TEACHING OF SPELLING. 

the pupil to use the words he has denned, in his own compo- 
tions. 

To conclude: Every Teacher must use his own experience 
and common sense. And so long as the Teacher has at heart 
the improvement of his pupils, he will continue to improve 
in the' "delightful task " of teaching the youthful mind. 



CHAPTER III. 

THE TEACHING OF GRAMMAE. 

Grammar* is the most difficult study of the common school 
room. Those, accustomed to teach only the more advanced 
pupils, know but little of the difficulties of teaching the ele- 
ments of language to children. Those who teach alone by the 
book, and the memorizing of rules, also know but little about 
it. To teach the elements of language to children, is not a 
trifling task. If, however, the right commencement is made, 
much labor is saved.f 

First, " teach one thing at a time, and be sure that one thing 
is learned, before another is attempted." This rule, so neces- 
sary in other studies, is particularly necessary in the study of 
Grammar. 

" By the old fashioned method of teaching Grammar, the 
pupil was required to commit the Grammar to memory with- 
out understanding it at all, or being expected to understand 
it, and then put to parsing all parts of speech at once." 

The Teacher's success in teaching Grammar, is, we believe, 
mainly dependent upon this one principle — " Teach one thing 
at a timer 

* By Grammar, is meant English Grammar ; that being- the only Gram- 
mar belonging to the Common School. 

t " Tower's Elements of Grammar " is an incomparable work for begin- 
ners. By its use the pupil acquires a knowledge of the principles of lan- 
guage before he commences the study of rules which he cannot under- 
stand, and prepares his mind for greater difficulties, 



o4 THE TEACHING OF GRAMMAR. 

Mr. Colburn says : " I have had scholars, who had learned 
their Grammar before they came under my care, so as to re- 
peat it by heart : yet, in parsing the word him, would call it 
in the nominative case, and still persist in doing so, after be- 
ing required to decline it five or six times in succession. — 
Arithmetic or any other subject furnishes examples enough 
of the difficulty of making scholars attend to the sense suffi- 
ciently to understand a rule or principle, when they have first 
committed it, without understanding it. But Grammar, per- 
haps, affords the most striking instances of it." 

At a public examination of my pupils, at which were seve- 
ral distinguished Teachers, I requested that some of those pre- 
sent should examine a class in grammar, Avhich had just con- 
cluded its exercises ; when the following question was given : 
"Notwithstanding his poverty, he was the delight of his 
friends." 

This being an example near the beginning of Smith's Gram- 
mar, (the text book used in my school,) was given as one 
which any child acquainted with the elements of grammar 
should answer. The class, though tolerably proficient in 
grammar, hesitated : but after a few seconds of thought, it 
was parsed. 

" NotivWistanding, a preposition, &c." "The word notwith- 
standing,'''' I remarked, "is a word difficult to parse; the rela- 
tion of the words shown by it, being somewhat obscure ; and 
resembling a conjunction in its relation to the sentence." 

"It is in the list of prepositions," was the reply. 

" That may be," I answered, but my pupils are not familiar 
with lists ; they parse by principle. 1 ' 1 

"But it is a fair example, being selected from the parsing 
exercises of Smith's Grammar." 

"Certainly," I replied, "the example is not at all unfair; 
I only offer these remarks to define the position of my pupils. — 
They are considered by their Teacher, well taught in the rudi- 
ments of grammar without regard to the order of the book, or 



THE TEACHING OP GRAMMAR. 35 

lists of words. If they have ever parsed that sentence, they have 
probably not fully understood it ; and consequently have not 
remembered the form. Had. they learned by the order of the 
book, and known the list of prepositions, to not know that the 
word just parsed, is a preposition, would be a defect : but in 
the present case, the defect would have been, to call it a prepo- 
sition merely from memory : and a much greater error than to 
say I don't know, I can't analyze it. As it is now parsed, the 
sentence is evidently understood." 

But, to proceed, — we will begin first, with the noun. Teach 
the pupil to understand that the name of every thing is a 
noun, and keep him at nouns until he is fully acquainted with 
them. Sometimes he will parse as nouns, words signifying 
quality or action : as the word good. 

"Well," says the Teacher, "what is a noun?" 

Ans. — "A noun is a name." 

"Name of what! a person, place or thing?" 

Ans.— "Of either." 

" Well, is the word good in your sentence, the name of a 
person?" 

Ans. — "No, sir." 

"Is it the name of a place ?" 

Ans. — "No, sir." 

" What is it the name of ? a thing ?" 

Ans. — "No, sir." 

" Then it is not a noun." 

Sometimes the pupil will answer, "it is the name of a thing." 

" Well, what kind of thing ? Did you ever see one ? — 
What is it like?" 

Ans. — " Yes sir, a good apple." 

" You may see the apple ; but it is the good that we are 
talking of: it is a thing of some kind whose name is good: not 
a good thing J" 1 Continue in this manner, until he is convinced 
that good is a word describing something, but not the name of 
the thing* So with other words. Sometimes he will call a 

*Note these words, and when he is at adjectives, remind him of them— 
they will assist him in understanding the nature of adjectives. So with 
verbs. 



36 THE TEACHING OF GRAMMAR. 

verb, as to write, a noun ; when the Teacher may proceed in 
the same manner as before. What kind of a thing is a, write V 
&c., &c. 

When the noun is fully understood, the pupil may com- 
mence with adjectives. Select the most simple adjectives, as 
sweet, sour, black, white, &c, qualities fully understood by 
the pupil. As he proceeds, he will make mistakes ; as " strike 
— an adjective, belonging to man" in the sentence — " I strike 
the man." 

"Well," says the Teacher, "what kind of man?" 

" Don't know." 

"Did'nt you describe the man?" 

" No, sir." 

"What does an adjective do?" 

"Describe." 

" Then strike, being an adjective, must describe the man. — 
What kind of a man is a strike man ?" 

'' Does it mean a large man, a small man, or — what kind of 
a man ?" 

" It does'nt say what kind." 

" Well, what does it say ?" 

"Why — it says, I strike* the man" 

" Then, as strike does not describe the man, it is not an ad- 
jective." 

Sometimes he guesses, as "tJwugh, an adjective." In such 
cases dismiss him for the present. For in no case must we 
permit the pupil to guess. And that he guesses, or knows 
nothing of the nature of an adjective, is evident. So proceed, 
until the adjective is understood. 

Next comes the verb. " A verb signifies to do.f If I strike 
a man, I do something, what then is the word strike f" 

" A verb." 

The Teacher should be careful to tell the pupil directly only 
as a last resort, and when the pupil will not think. Every 

* Let the Teacher take note of this, to use when he comes to verbs, 
t Neuter and passive verbs may be omitted at thi3 time. 



THE TEACHING OF GRAMMAR. 37 

thing snort of direct assistance may be given, but, as Page 
says, " let the pupil achieve the final victory." Leave some- 
thing for himself to do ; and be it ever so little, he will feel a 
satisfaction in discovering it himself. He should now be re- 
ferred back to the adjective strike. Suppose the pupil parse 
the word happy in the sentence ; — " He is happy," as a verb;* 
let the Teacher, recur again to the verb, to strike. He knows 
that strike is a verb, because it is to act, — to do. " Well," says 
the Teacher, " does to happy mean to do ? In what manner 
do you happy a person. You know how to strike a person, 
I suppose ; how would you happy him ?" 

Let the Teacher conjugate it thus — ( "I happy, 

You happy, 
or thou happiest, 
He nappies." 

and if the pupil has not mind enough, or it is not waked up 
sufficiently to see the absurdity, his Teacher has not done much 
for him. Having convinced him that happy is not a verb, let 
him understand that he is a happy man, and if he does not 
know that happy describes the man, there is room for doubt 
respecting his knowledge of adjectives. 

The precise order of teaching number, person, gender and 
case, the moods, tenses, &c, the other parts of speech and their 
sub-divisions, together with their various relations, must be 
left mainly to the judgment of the Teacher. Even after the 
pupil has advanced beyond the rudiments, he sometimes calls 
words, nouns which are not names. In my experience I find 
it profitable sometimes to render the pupil's parsing ridiculous, 
even to himself. Thus when he parses such a word as 
virtuous, a noun, I let him proceed through person, number, 
gender, &c. 

"How do you know it is masculine gender?" the Teacher 
asks. 

"Because," answers the pupil, "it is a male." 

* These exercises the Teacher will perceive are in accordance with the 
common system of Grammar : they are, however, applicable to all. 



38 THE TEACHING OF GRAMMAR. 

" How do you know ? Did you ever see one ?" " One 
what ?" asks the pupil. 

" A virtuous," answers the Teacher. 

"I've seen a virtuous wan," continues the pupil. 

"Man!" echoes the Teacher, "is that the word we are 
parsing ? Did you ever see or hear of a virtuous ?" 

The following example occurred in my school to-day, and 
while it is fresh in my memory, I record it. 

" The dinner tvaits, and we are tired.' 1 

" Tired, a noun of the third person, singular number, neuter 
gender." 

" Why is it neuter gender ?" 

" Because it is neither male nor female ?" 

" How do you know it is neither male nor female ?" 

" I know it," repeated the pupil with confidence. 

" How do you know it ? Did you ever see one ? Is tired 
the name of any thing ? If it is, please to describe it." 

" Well," -persisted the pupil, it is certainly neuter gender." 

"That it is wo gender," said the Teacher, "is true, but you 
say it is a thing of the neuter gender, a thing called a tired, a 
thing which neither you nor I, nor any person ever heard of." 

Frequently the pupil will parse such words as love a noun, 
when it denotes action, and a verb, when it is a name, for want 
of fully attending to the sense, or more properly for want of 
thinking. The remedy in such cases, is to wake up his mind, 
make him think. 

By teaching thoroughly as you proceed, the intellect of the 
pupil must be dull, if he obtains not a tolerable knowledge 
of the principles or elements of Grammar. 

That pupils are not taught more thoroughly, is, probably 
often owing to the Teacher's own deficiency. Many Teachers 
do not possess more than the elements, themselves; and of 
those who do, how few speak correctly in their conversation I 
To teach his pupils Grammar, a Teacher should be not only a 
pattern of correct conversation, himself, but he should notice 
every violation of correct language that he witnesses amongst 



THE TEACHING OF GEAMMAR. 39 

his pupils, either in their writing or speaking. Avoid all 
cant phrases, and provincialisms. I once heard the Principal 
of a flourishing Academy — a Teacher of ancient and modern 
languages use the following language : 

" A whole parcel of my scholars once ran off to and 

got into mischief." After describing the mischief, &c, he pro- 
ceeded — "But 1 found them out ; and I guess I learned them 
better than to get into such a scrape again." 

Now, this sentence can be parsed according to the rules of 
Grammar. It violates no special rule of syntax, except in 
the word got. Parcel is the subject of the verb ran, and lohole 
is an adjective, describing it. This parcel, (not a part of a 
'parcel, but the whole parcel) ran off of something. He learned, 
not taught them, &c; to get is a transitive verb denoting to 
procure, to obtain, &c, but its general use as an intransitive 
verb may sanction this corruption. 

A Teacher who uses such language as the following to his 
pupils, is unfit to be in a school-house, except to learn : 

" Joseph I know you done it, I seen you do it, and I have 
often saiv you do it. Now set up, and write your copy. Have 
you wrote a copy to-day '?" 

It is hardly necessary to speak of those who habitually 
violate the ordinary rules for the government and agreement 
of nouns and verbs. They had — "better ta'en up spades and 
shools, or knappin hammers." 

The office of Grammar is to teach us to speak and write 
correctly, to arrange words and sentences with propriety, and 
not merely to know to what parts of speech they belong ac- 
cording to a particular system of Grammar. Thus, the word 
but as except, is by some called a conjunction, and by others — 
a preposition. But whether a preposition or a conjunction, it 
is of but little consequence, if he fully understands its import, 
so long as the best writers disagree as to its name. It is enough 
for the pupil to fully comprehend the distinctions of but little 
is done, John may go but you must stay, and all but you may 
go. If but in the last sentence is called a conjunction, he will 



40 THE TEACHING OF GRAMMAR. 

see that its relation to the pronoun you which follows it, is very 
different from the relation of the real conjunction hut to the 
pronoun you, in the second sentence. No matter from what 
word or words it may have been derived, it, as now used, has 
a different meaning. If called a preposition he will see that 
it does not show that relation to words that prepositions usually 
do ; yet as the nature of its government seems to require the 
objective case to follow it, as except him, excepting, or leaving 
out him, its name is of but little importance. If, in accordance 
with the views of some writers, the nominative case should 
follow it, it must be parsed a conjunction. Custom, however, 
(or what is called good usage) which gives law to language, 
decides all such disputes. 

The definitions* of the various parts of speech, their num- 
bers, persons, genders, moods, tenses, &c, should not be learned 
by the pupil until he understands these divisions without their 
names. No matter what may be the system taught, whether 
Cardell's with three parts of speech, or Murray's withten; 
no matter whether 3 tenses or 6 ; the same divisions of our 
language exist, and must he taught, no matter what may be 
their names, and much better without the written definitions 
than with them.f As no pupil can understand a definition 
without its application, it is better to teach the application first, 
and afterwards the definition.^: But the rules for the arrange- 
ment, agreement and government of words, being wholly 
arbitrary, not being founded on any principle, must be com- 
mitted to memory, and committed well.§ " An active transi- 

* The same should be observed with the definitions and rules of arith- 
metic. 

f As to the different systems I recommend none. Every Teacher 
should judge for himself. " Green's Analysis" is an excellent work. 

X Smith's mode in the beginning of his work, is very good. 

? It is said by some that " Grammar should be taught upon the principles 
of language, and the meaning of words, instead of mere rules, founded 
on no correct principle of language." This would be true, if the gram- 
marian's " province were to give law to language," but as it is an admitted 
fact that the grammarian's province is only to teach the language in ac- 
cordance with the sanction of good usage, i. e. good, general, reputable 
usage, and that the rules which govern it, and which we must teach, are 
binding upon us, we, as practical Teachers, must teach it as it is. 



THE TEACHING OF GRAMMAR, 41 

tive verb governs in the objective case," not as a rule of mathe- 
matics, but because it does : because the book says so, upon the 
authority of good usage. Therefore, as no reason why him 
should not be he, can be given, but an arbitrary rule without 
reason, it is absolutely necessary that the rule be impressed 
upon his memory. * The time when these rules are committed 
depends upon the system of teaching. 

I will close this Chapter with a few practical examples from 
the experience of the School room. 

PRACTICAL EXAMPLES. 

Pupil. — " Is is a neuter verb." 

Teacher. — " Why is it a neuter verb ?" 

P. — " Because it does not express action, but simply being." 

P. — " Sit is a neuter verb." 

T. — " Why is it a neuter verb ?" 

P. — " Because it denotes simply being." 

T. — " When you sit on the chair, do you not act to keep 
yourself in a sitting posture ?" 

P.— "No sir." 

T. — "If you were to faint or sleep, would you still sitV 

P.— "No sir, I would fall" 

T. — "Then, you use action to sit on the chair?" 

P.—" Yes sir." 

T. — " And to stand on the floor ?" 

P.— "Yes sir." 

T. — " How then is sit a neuter verb ?" 

P. — " I don't know. I suppose it is merely so called." 

" That is a good idea," continued the Teacher, " names are 
unimportant : and whether we call all verbs active, as Car- 
dell, (who is compelled to make the same distinction by another 
name,) or call all intransitive verbs neuter, as Murray, who 

*I would, however, as in mathematics, avoid a multiplicity of rules. — 
Murray and his copyists extend the simple rule " a verb must agree with 
its nominative, in number and person," into half a dozen rules. The rules 
that " the subject of a verb must be in the nominative case." " Preposi- 
tions govern the objective case," " active transitive verbs govern the ob- 
jective case " — are also extended into a rule for relative pronouns, one for 
the conjunction "than" — &c, &e. 



42 THE TEACHING OF GRAMMAR. 

is also compelled to divide his neuter verbs into two classes, 
yet the distinction exists. According to the idiom of our 
language, and good usage, they are a distinct class of verbs, 
whether we call them neuter or not, and are distinguished by 
always having the same case after them as before them."* 

"Are sit and stand, always neuter verbs?" 

"Not always. If they do not denote action, grammatically 
they have no action, and are parsed neuter verbs. To sit or 
stand when denoting action as sit still, sit up or stand erect, 
are active verbs, and are so used by good authors. But when 
they denote merely position, as the man sits (is) on the chair, 
the table stands (is) on the floor, they are used as neuter verbs. 
Notwithstanding there is action in sitting, yet when the word 
is used merely to denote his position on the chair, it is distinct 
in its signification : therefore, we will parse them neuter verbs. 
The same rule is applicable to other verbs as to look, to smell, 
&c. The clouds look black, the rose smells sweet, denoting no 
action, and I smell the rose, and look at the clouds denoting 
action."f 

EXERCISES OF SECOND CLASS. 

"I have ruined my friend." 

" Have is a verb " — says scholar, No. 1, of the indicative 
mood, perfect tense, agreeing," &c. 

The next one takes up ruined and parses it in the same way- 
The Teacher says, "not correct : pass on to the next." 

A pupil at length discovers that the two words have and 
ruined should be parsed together. 

"No," says the Teacher, "you have separated them and 
they must remain so. Every word in our language has a 

*To dispute with Cardell -whether all verbs are active, is not teaching 
Grammar ; and to dispute, as some authors, do with Murray, whether to 
walk and to run are active or neuter verbs, is mere trifling. 

t " The man falls from the chair." Falls is parsed an active verb, although 
the body of the man is strictly passive, the action is performed on him by 
the attraction of the earth ; yet, grammatically, the man falls, and to fall 
is to act, in accordance with the structure of our language, as much as to fly. 



THE TEACHING OF GRAMMAR. 43 

distinct meaning ; and to permit you now to connect the two 
words, would be an admission that they cannot be parsed 
separately."* 

" Have " and " ruined" are at length parsed separately ; they 
are next parsed together, and the difference .explained between 
have as an auxiliary and as a principal. 

"Is written," is next parsed conjunctly and separately. 

"He is not volatile," is the next sentence. 

"Not," says one of the class, "an adjective describing the 
noun volatile." 

"What kind of a volatile is a not volatile?" asked the 
Teacher. 

" A not volatile !" repeats the pupil with surprise. 

" Yes," continued the Teacher, " an adjective describes a 
thing. Is the thing a good, a bad, or a not — thing ?— or knotty, 
perhaps you mean.f A knotty volatile ! Is that it ? Will 
you tell me what a volatile is?" 

" Volatile is not a noun," replied the pupil. 

" Then not is not an adjective," said the Teacher, who 
demonstrates by various examples the absurdity of parsing 
not as' adjective in any case even when it is placed before a 
noun. »• 

One of the class parses " volatile " as a verb ; the Teacher 

conjugates the verb "I volatile, 

Thou volatilest, 

You volatile, 

He, she, or it volatiles." 

" He taught me grammar." 

We are now in another class. 

T. — " Was it I or Grammar that he taught." 

A. — "He taught grammar to me." 

T. — "Will you change the verb taught to a passive verb?' 

P. — "Grammar was taught to me." 

*This is intended to impress upon the pupil's mind that every word has 
a distinct meaning of its own. 

f This renders the incorrect parsing of adjectives so ridiculous that it 
improves the pupil very soon in that respect. 



44 



THE TEACHING OF GRAMMAR. 



T. — "Will you parse I was taught grammar?" 

P. — " Was taught, a passive verb — ." 

T. — " What is the nominative case to a passive verb ? The 
subject or object ?" 

P.— "The object." 

T. — " But grammar is the object, and was taught to me. — 
The pronoun me is the object of to." 

The class can go no further : but their desire to know i s 
aroused ; and I am sure of an audience. 

In plain English, then, the phrase is sanctioned by good 
usage and by all grammarians, which, of itself, according to the 
present law of language, is a sufficient reason for its use. If, 
however, it is not sanctioned by some regular law of language^ 
it belongs to the list of anomalies or idioms as 

" The cloth is worth six dollars a yard. 

The wall is 20 feet high. 

The goods are selling."* 

" But," I continued, " He taught me,f i. e. I was taught. — 
So was grammar taught and when they come together in the 
same sentence, one must be taught to the other ; as two persons 
are introduced — one to the other : I introduce both, and eithe r 
may be the nominative to the passive verb, the other remain- 
ing of course in the same case after the passive as it was be- 
fore — with the transitive verb. The rule says that ' a passive 
verb sometimes governs the objective case.' But it has a 
reason for its government."^: 

It is not profitable to dispute with authors of text books to 
your pupils. Better explain their principles and compare 
them, leaving the pupils to judge for themselves. One of my 
pupils once asked me which of the following sentences is the 
most correct : 

* This idiom is sanctioned by Goold Brown and others. 

f We might argue from the Latin, that " / was taught grammar" was 
correct in English were it justifiable. 

% This is one example of many to show the mode of thorough explana- 
tion. 



THE TEACHING OF GRAMMAR. 45 

"If I was in town," 

" If I were in town." 
Instead of deciding, I wrote several sentences of the subjunc- 
tive mood, as 

" If he were in town, I would go and see him." 

" If he was there, I did not see him." 

" If he be good, he will be happy." 

" If he is good, I am deceived," 
and compared them with the same sentences without variation 
according to some innovators, and explained to him the two 
systems as taught by different authors. 

FIRST CLASS — EXAMPLES IN PARSING. 

He is noble. 

T.— " What is an adverb f" 

P. — " An adverb is a word used to qualify a verb, &c." 

T. — " What is an adjective?" 

P. — " An adjective is a word used to describe a noun." 

T. — " Would you say, He is noble, or He is nobly V 

P. — " Noble : a noble man, or noble person." 

T. — "He works noble, or nobly?" 

P. — "Nobly, because it describes how he works." 

T. — "His work is well, or good?" 

P. — " Good, because it is good work." 

T. — "He works good or well ?" 

P. — " Well, because it describes how he works." 

T. — " Can an adverb qualify a neuter verb?"* 

P.—" Yes, sir, He is there." 

T. — "An adverb of manner, can never qualify a neuter 
verb nor has a neuter verb any adverb, really belonging to it. 
In the sentence, He is there, there more properly belongs to he : 
but as the word there cannot describe a noun, we call it an ad- 
verb. If it could describe a noun, the verb is would change 
it to an adjective, as 

He works well, 

*I repeat here, that it matters not whether the term neuter is correct, or 
not ; the distinction must exist by some name. 



46 THE TEACHING OF GRAMMAR. 

He is well, 
either of which is correct : but you may not say, He is nobly- 
You cannot correctly say, He works good ; but you may say, 
He is good. 

He is high. 

P. — " High is an adjective, &c." 

He flies high. 

P. — " High, an adverb," &c. 

Teacher — " Does the word high denote the manner of flying ? 
Or does it describe the situation of the bird? The bird is high. 
Here, you see that after the verb is, it is an adjective without 
cavil but after the verb fly, it is not so clear to your mind. 
Why ? Because an adverb cannot denote the manner of a 
neuter verb, and an adjective cannot qualify any verb : and 
as high is evidently an adjective without regard to position in 
the sentence, and can be used only to describe something : if 
intended to describe the manner of flying, it is incorrect." 

Pupil — " High is an adjective, describing bird." 

Teacher — " Or, the situation of the bird." 

The Dog looks wicked. 

P. — " Wicked, an adjective describing dog." 

T.— u May it not qualify the verb looks." 

P. — -"No sir, wicked is an adjective, as high, and must de- 
scribe something-." 

T. — "But wicked is different from high in this respect. — 
When we say the bird flies high, we know the word high to be 
used to denote the position of the bird : for the adverb highly 
which denotes the manner of some verbs, cannot denotes the 
manner of flying. To fly highly would be absurd: whereas 
the clog may look wickeldy at you. It therefore depends 
upon your meaning, whether you use wicked or wickedly. — 
If the dog looks (is) a ivicked dog, wicked is an adjective describ. 
ing dog ; if you intend to denote his manner of looking at you, 
it should be wickedly." 

P. — " How then are we to know whether the sentence is 
correct or incorrect ?" 



THE TEACHING OF GRAMMAR. 47 

T. — " We must presume it to be correct, and that the auth- 
or (being a correct writer) means to describe the look of the 
dog. I will give an illustration. The phrase He has wrote, is 
absolutely incorrect; but He has loved, may be either correct 
or incorrect, according to the author's meaning. In reading 
a sentence of this kind unconnected with other words, we 
must presume the author to be a grammarian, and parse it 
accordingly. The author unacquainted with grammar, some- 
times means what he does not say : and therefore a speaker 
should be acquainted with the language which he attempts to 
speak or write. Wicked, therefore, in this sentence, is an ad- 
jective ; and looks, a neuter verb." 

The clouds look black. 
The rose smells sweet. 

P. — "Look and smells are then neuter verbs ?" 
T. — " They are. Look denotes nothing more than the ap- 
pearance of the clouds, which look (are) black, and smells the 
perfume of the rose. 

The person who smells acts, but he cannot sweet smell the 
rose : he might smell it sweetly, if there were any meaning in 
the phrase. 

THIED CLASS. 
John took a handful of ashes and threw them into the stove. 

T. — " Where is this sentence incorrect ?" 

No answer. 

T. — " John fell down 7 and hurt herself." 

Now, any child detects instantly the error in this sentence. 
" Pronouns must agree with the nouns for which they stand in 
gender number, and person." 

By suitable explanations, the Teacher easily illustrates to 
the pupil, that the former sentence violates the same rule as 
the latter. 

Some wit called clear blank paper, every infant mind. 

T. — "This means simply that some witty person compared a 



48 THE TEACHING OF GRAMMAR. 

child's mind to blank paper: i. e called it blank paper. Do you 
now understand it."* 

The boy fell and cut his lip on the ice. 

The red cow and the fat pig were in the yard. 

John has a new coat, and a white hat. 

William bought a top with the money which was given him by 
his father. 

These sentences are suitable for young pupils, and any one 
who has been taught to understand a noun and a verb, can 
parse them rapidly. As the pupil advances in knowledge, 
make the sentences less simple ; but, by no means permit him 
to parse language he does not understand. The Teacher may 
understand very well, such a sentence as 
" Mighty one all hail ! I joy to see thee on thy glowing path: stern, 

unwearied, resolute" 
but the child probably does not. 

I will close this Chapter by a few exercises of the first class. 

Every person should be careful of their reputation. 

P. — " Their is incorrect, because it is a pronoun of the 

plural number, and the noun person which it represents (or for 
which it stands) is in the singular number, but the rule says, 
A pronoun must agree with the noun for which it stands, in 
number, person and gender. Therefore, their should be his : a 
pronoun of the singular number, agreeing with person, &c." 

T. — "In what number, person and gender, is person f n 

P. — " Singular number, third person, common gender.f 

T. — " Will you parse the pronoun?" 

P. — " His is a pronoun of the singular number, third per- 
son, masculine gender." 

T. — " They do not, then, agree in gender." 

P. — " Common Gender." 

* Much time is often lost to the pupil by permitting him to parse what 
he cannot understand, or trying to parse it. 

t We will not dispute with those who deny the Common Gender. "The 
thing we call a rose, by any other name would smell as sweet." The dis- 
tinction exists, call it by what name you please. 



THE TEACHING OF GRAMMAR. 49 

Another Pupil — " There is no pronoun in our language, of 
the common gender. It should, therefore, be his or her repu- 
tation" 

T. — " Sis or her is what is denoted by what is called com- 
mon gender, but it is denoted by no pronoun in our language. 
What are the pronouns denoting gender ?" 

P. — " He, she and it, masculine, feminine and neuter." 

T. — " There being no pronoun denoting the common gen- 
der, his or her would be correct, but that custom i. e. good usage 
has established the pronoun his. This pronoun denoting a 
person without regard to sex, as man is frequently used to 
denote mankind." 

" Will you please to let Sarah and I go for water?" asked a 
little girl belonging to my grammar class. 

" Will you parse the word go, before you go ?" I asked. 

" Go is a verb — " 

" Well, — go on. Is it active or neuter ?" 

" Active." 

"Transitive or Instransitive ?" 

" Intransitive." 

" What mood and tense?" 

" Indicative mood, present tense, agreeing with its nomina- 
tive Z," &c. 

" Where did you obtain the IV I asked. 

" /should be me" I replied : "and is the object of the trans- 
itive verb let." 

I proceeded until she parsed it correctly : when she went 
for her water. 

" I am industrious that I may be rich." 

" He is so industrious that he will be rich." 

" I knew that he would be rich." 

" That man is rich." 

" That was a rich man's house." 

" He that is industrious will be rich." 

" That he is rich is believed by all." 

" That that I said was, that he was rich." 



50 THE TEACHING OF GRAMMAR. 

" That that that man said was that he was rich." 

" He said that that that that man said was not that that I 
said. 

" That that I said was this : that that that that that man said 
was not that that that I said. 

"Not that I loved Brutus less, but that I loved Eome 
more." 

" It is evident that he is poor." 

" I know not but that he was rich." 

"But that I am not able, I would do it so that it would 

last." 

" That he ought to do it, is proved by this fact. 

"Why is it that he is poor?" 

" We hold this truth to be self-evident, that all men are cre- 
ated equal." 

" It is such that" &c. 

These last exercises, many more of which might be given, 
are practised with the advanced classes, to teach them thor- 
oughly, the signification of a word, without respect to gram- 
matical names. Some of our text books say — " That is a re- 
lative, when who or which may be substituted for it." 

" That is a demonstrative, when it is joined to a noun, to 
point it out." 

" That is a conjunction in all cases, when it is neither a re- 
lative, nor a demonstrative." 

This is a very good classification ; yet it is evident that the 
word " that" when it is neither a relative nor a demonstrative: 
and is according to the books — a " conjunction," has different 
significations. In many examples it plainly represents a 
phrase, and in others it is only a connecting word : and to ex- 
plain such words fully to the pupil, the teacher must place 
the word before him in a variety of examples. 

To prolong these exercises, would make a treatise on the 
science, rather than the teaching of it. I will, therefore, leave 
it with its imperfections, to the judgment of my fellow 
Teachers. 



THE TEACHING OF GRAMMAR. 51 

We will append to this Chapter, an extract from an article 
of the Compiler's, from the Pennsylvania School Journal : 

As the pupil advances in grammar, we should endeavor to 
teach him to avoid the idioms of his particular neighborhood. 
These errors appear not only in his conversation, but in his 
composing lessons. Many of these are of a kind, not reached 
by the regular Grammar rules, as more nor that, — the ink is 
all, — he is got to do it, — he is got it done, — he is got a book, — 
if he had have done it,- — if I ivould have knoivn it, I would 
have told you, $c, $c. Others are violations of positive rules? 
which being often used in good society, are more likely to be 
imitated, than more vulgar errors, as between you and I, — 
Please to let James and I go for water, — I saw John Smith, he 
who owns the black horse tavern, — I done it, ho,.-, &c. 

Such errors, all of which are common in many places, should 
be particularly pointed out to the pupil, during his progress 
in study. 

Let thorough explanation be the Teacher's motto, which 
may be illustrated by the following example of parsing : 

Pupil (reads) — " The man whom you saw, perished in the 
snow." 

Pupil — " WJwm is a relative pronoun " — 

Teacher. — " Why is it a relative pronoun ?" 

P. — " Because it stands for the noun man." 

T. — " In what case is man ?" 

P. — " Nominative case." 

T. — "In what case, person and number is whom?" 

P. — " Objective case, third person, singular number, agree- 
ing with man." 

T. — " Why is it in the objective case ?" 

P. — "Nominative who, possessive whose, objective whom. 1 ' 

T. — " What is the meaning of objective case?" 

P. — "The object of a transitive verb, participle or preposi- 
tion." 

T.— "What is whom the object of?" 

P. — " Of the verb perished." 
4 



52 THE TEACHING OF GRAMMAR. 

T— l < Who perished ?" 
P.— 1 ' The man." 

T. — " Perished what ? "What did the man perish ?" 

No answer. 

T. — " If whom were ivho in this sentence, in what case would 
it be?" 

P. — "Nominative case." 

" No," interposed another pupil, " who is incorrect." 

" Why," asked the Teacher, " would it be incorrect ?" 

" Because, it should be the objective case," was the reply. 

" Why should it be the objective case ?" 

" Because it is the object of " (a pause.) 

"Why should it be the objective case?" reiterated the 
Teacher, " can any one answer ?" 

"Because it is the object of the verb saw" was, at length 
answered. 

" The man whom I saw," continued the Teacher, " Whom 
did I see ?" 

P.—" The man." 

T. — " Is man the object of saw ? but, you have already 
parsed man in the nominative case." 

P. — "No, whom is the object of saw." 

T. — " Then, man is not the object?" 

P.—" No, sir." 

T. — "I did not see the man." 

Pause. — "Yes sir," answered several voices. 

T. — "It appears that you all know that the pronoun whom 
is in the objective form ; but as you do not know that it is 
the object of any verb, participle, or preposition, you do not 
know that it is in the objective case. One of you said that 
if whom were who it would be in the nominative case ; another 
said, who would be incorrect. Now as you all appear to judge 
the case by the form, the former is right ; for who is in the 
nominative form, and is only incorrect when it is not in the 
corresponding case ; which none of you can say it is not. — 
You know only the form, as learned from your books ; and 



THE TEACHING OP GRAMMAR. 53 

judge the case by it alone. Now let me explain. ' The man 
whom or that I saw perished/ clearly expresses that the man 
was seen by me ; but as the word man is already nominative, 
it cannot be objective, also : i. e. grammatically, although it i s 
philosophically, the object of the verb saw. Therefore, the 
pronoun that or whom is used to represent the noun man, to 
be governed by the verb, instead of the noun itself. And as 
relative pronouns are used to connect sentences,* it is placed 
before the governing word, to connect it with the preceding." 

* The true definition of a conjunction is a word that connects and con- 
nects only. 



CHAPTER IV. 

THE TEACHING OF ARITHMETIC. 

Warren Colburn, at a Convention of Teachers held in 
Boston, said : 

" By the old system, the learner was presented with a rule 
which told him how to perform certain operations on num- 
bers ; and when these were done, he would have the proper 
result. But no reason was given for a single step. His first 
application of the rule was on abstract numbers, and so large 
that he could not reason on them, if he had been disposed to 
do so. And when he had got through, and obtained the re- 
sult, he understood neither what it was, nor the use of it. — 
Neither did he know that it was the proper result, but was 
obliged to rely wholly on the book, or more frequently on 
the Teacher. As he began in the dark, so he continued ; and 
the results of his calculation seemed to be obtained by some 
magical operation, rather than by the inductions of reason. 

" Let him commence," he continues, " with practical exam- 
ples, in which the numbers are so small that he can easily rea- 
son upon them. And the reference to sensible objects, gives 
him an idea at once of the kind of result which he ought to 
produce, and suggests to him the method of proceeding neces- 
sary to obtain it. By this, he is thrown immediately upon 
his own resources, and is compelled to exert his own powers. 
At the same time, he meets with no greater difficulty than he 
feels himself competent to overcome. In this way, every step 
is accompanied with complete demonstration. Every new ex- 
ample increases his powers and his confidence. Most scholars 



THE TEACHING OF AEITHMETIC. 55 

soon acquire such a habit of thinking and reasoning for them- 
selves that they will not be satisfied with anything which they 
do not understand, in any of their studies. 

"Instead of studying rules in the book, the reason of which 
he does not understand, the scholar makes his own rules ; and 
his rules are a generalization of his own reasoning, and in a 
way agreeable to his own associations." 

The operations in this stage of a child's studies (which we 
call No. 1,) are mostly confined — in my experience — to ques- 
tions involving small numbers, easily understood, and inde- 
pendent wholly of rules. Mental arithmetic may be com- 
menced at any time, and continued through the whole course 
of his studies. 

Nor should the pupil in his first studies, be permitted to 
work out questions by any rules. Let him use such books as 
Colbubn's or Stoddaed's Mental Arithmetic, or Gbeen- 
leaf's or Davies', or, which is better, let the Teacher him- 
self give promiscuous examples involving the various princi- 
ples. How often have we known pupils, taught in the old 
way, who could do every question under the heads of addi- 
tion, subtraction, multiplication and division ; but who, when 
given a question without a rule, would ask, " Must I multiply 
or divide, add or subtract ?" 

If he knew the answer, he would perform operations until 
he obtained it, if he could ; or, if he could not obtain it, by 
" hook or crook," ask the assistance of the Teacher ; and be sa- 
tisfied with the performance, without caring to understand it. 
Such pupils, as they proceed, cease, more and more, to reason, 
until they cease to think, altogether. In the " Eule of Three," 
for example, he will state the question in different forms, until 
he obtains the answer : when he is satisfied with haviug per- 
formed an operation, and obtained an answer, neither of which 
he understands. If required to perform it by the rule, he 
"writes the same name or kind as the answer (in the book) in 
the third term." He " considers from the nature of the an- 
swer in the booh, whether it is to be greater or less than this 
third term." 



56 THE TEACHING OF AEITHMETIC. 

Thus he continues in the dark, until he is through the book, 
without understanding a principle of arithmetic. In a school 
I lately visited, a boy calculated the interest on 15 dollars, at 
5 per cent. — by multiplying 15 by 5 — making 75 the answer: 
but whether dollars or cents he couldn't say. He had gone 
on until he had reached the answer, (which was merely 75,) 
and that was enough. 

I once had a pupil, a little girl, who was always satisfied 
with the operation performed by the Teacher, without asking 
a question. I had in vain labored to make her think. To any 
explanation, she was heedless ; and either with or without it, 
equally satisfied. The instructions of her Teacher, she impli- 
citly obeyed, without judgment, or even a thought. A sim- 
ple expedient often wakes up the mind. She was required to 
reduce feet to inches on the blackboard. As usual, she could 
do nothing ; and I told her to divide by 3 because 3 feet were 
in a yard. Seeing her do that so readily, I directed her to 
divide by 12, the number of inches in a foot. It was done 
without hesitation. "Multiply by 144 — the number of square 
inches in a square foot, and," I continued, prompted by curio- 
sity to see how far she would follow without suspicion, "di- 
vide by 9 the square feet in a yard." I then led her through 
troy weight and several other tables, and she was about to 
multiply by 365| days, when the class, who could be restrain- 
ed no longer, burst into a hearty laugh. She stopped, turned 
around with a bewildered look upon the class, then at the 
Teacher, and as if her ridiculous performance had suddenly 
flashed upon her mind, she burst into tears, and sank sobbing 
into her seat. 

" Oh, Mr. Lamborn," said she, " why did you tell me to do 
that?" "Why not?" said I, "you would have had the an- 
swer shortly. You are mostly satisfied with any operation 
that brings the answer." After that time, whenever she was 
disposed to take an operation upon the word of her Teacher, 
or the answer, I would ask her if she remembered the black- 
board. This was hint enough. She would then think. 



THE TEACHING OF ARITHMETIC. 57 

A young lady who had gone through " Emerson's Second 
Part," entered my school as a pupil. The questions in this 
book, having no answers, I expected to see principle and judg- 
ment. She couldn't work for answers. But I found that a 
pupil not taught to think, may be taught even worse (if pos- 
sible) than he who works solely for an answer. Without 
thought, — without answers, she had no guide. She added, 
subtracted, multiplied and divided by random. Depending 
upon the Teacher, she worked wholly in the dark. I will il- 
lustrate her case by an example. Her question was, " What 
is the interest of a certain sum at 7 per cent, per annum, for 
5 months ?" I obtained the interest for one year, which I di- 
vided by 12 to obtain the interest for a month : I then multi- 
plied the interest for one month by 5, to obtain the interest for 
5 months. All this I explained thoroughly. 

The next question, was the discount of a sum for 4 years 
and 7 months — reckoning lawful interest. She multiplied by 
7, as I had done, divided by 12, and multiplied by 4 ; and 
when asked why she did so, she replied because I had so work- 
ed the other question: but, whether discount, interest, or 
amount was what she had, had not entered her mind. She 
could not even say, " I have the answer :" but very innocently 
answered, " I am trying to do the question." 

Who is to blame for this inaction of the pupil's mind ? The 
Teacher who directed his first studies. It is much easier for 
the Teacher to tell a child how to perform an operation and 
still more easy to perform it himself for the child, than to teach 
him to understand it. I hold the doctrine that a Teacher 
should never solve a question for a pupil. Neither should he 
tell him directly how to do it. 

" If the learner meets with a difficulty," says Mr. Colburn, 
"the Teacher should examine him, and endeavor to discover 
in what the difficulty consists ; and then, if possible, remove 
it. Perhaps he does not fully understand the question. Then 
it should be explained to him. Perhaps it depends on some 
former principle, which he has learned, but does not readily 
call to mind. Then he should be put in mind of it. Perhaps 



58 THE TEACHING OF ARITHMETIC. 

it is a little too difficult. Then, it should be simplified. But 
by no means should the learner be told directly how to do it ; 
for then the question is lost to him. He is perfectly satisfied 
with it, and will give himself no further trouble about the 
mode in which it is done. When the learner requires assist- 
ance too often, it is an indication that something has not been 
learned thoroughly ; and he then should go back to some 
place, that he does perfectly understand, and review. 

" Do not simplify practical examples by means of abstract 
ones. For example, if you propose to a child this simple 
question : " George had five cents, and his father gave him 
three more, how many had he then ? I have found that most 
persons think to simplify such practical examples by putting 
them in an abstract form, and saying, How many are 5 and 3 ? 
But, the question is already in the simplest form that it can 
be. The only way that it can be made easier, is to put it in 
smaller numbers. If the child can count, this will hardly be 
necessary. No explanation more simple than the question 
itself can be given, and none is required. The reference to 
sensible objects, and to the action of giving, assists the mind 
of the child, in thinking of it, and suggests immediately, what 
operation he must perform; and he sets himself to calculate it. 
Most persons, when such a question is proposed, do not observe 
the process going on in the child's mind ; but because he does 
not answer immediately, they think he does not understand 
it, and they begin to assist him, as they suppose, and say, How 
many are five and three f Cannot you tell how many five and three 
are ? 

"Now, this latter question is much more difficult for the child 
than the original one. Besides, the child would not probably 
perceive any connexion between them. He can very easily 
understand, and the question itself suggests it to him better 
than any explanation, that the five cents and the three cents 
are to be counted together ; but he does not easily perceive 
what the abstract numbers, five and three have to do with it. 
This is a process of generalization, which it takes children 
some time to learn." 



THE TEACHING OF AEITHMETIC. 59 

The second stage {Number 2) is the arrangement of Avhat he 
has learned into rules ; which will be much more readily re- 
membered than when committed to memory without under- 
standing them. The operations on large numbers may now 
be demonstrated. By rules, we do not mean all the rules the 
text-book may contain, but a few general rules ; avoiding, as 
much as possible, special rules for special questions, as hin- 
drances to the making of thorough scholars. But what rules 
would you call general, and what special ? This depends upon 
the method of teaching. Let us cast our eyes over the page s 
of some of the modern popular School books. In Smith's 
Arithmetic, we are told to multiply by .4, by .3, by .375, by 
5(j, by 9 , &c, to reduce Federal money to absolete currencies 5 
and as many more rules to change them again to Federal 
money, with examples under each rule. Who would permit 
his pupils to waste their precious time with such stuff.* 

To multiply a fraction by a whole number, 
" " whole number by a fraction. 

" " one fraction by another, 

To add fractions, 

To subtract fractions, 

To divide a fraction by a whole number, 

To divide a whole number by a fraction. 
" " one fraction by another. 

To reduce whole numbers to fractions of a greater denomi- 
nation. 

To reduce fractions to whole numbers of a less denomination. 

To reduce fractions of a higher denomination to a lower. 
" " of a lower denomination to a higher. 

* Although we so emphatically condemn the application of rules to 
practical" questions, without demonstration, or before the pupil's mind is 
sufficiently matured to comprehend them, yet we think it unnecessary to 
postpone the operations of the primary rules on abstract numbers, until 
the pupil is fully acquainted with their application to practical questions : 
nor is it even necessary that he know that there is any connexion between 
these. In plain words, a child may be taught to perform operations in ad- 
ditions, subtraction, multiplication and division, before he is acquainted 
with any principle ; merely as a mechanical performance. The first ex- 
ercises in the tables are merely mechanical, and are learned before they 
are understood. The pupil, however, should neither apply these operations, 
nor the tables, -to practical questions, until he can demonstrate them. 



60 THE TEACHING OF ARITHMETIC. 

Then follows Addition, Subtraction, Multiplication and 
Division of Decimals. 

These are all special rules. The pupil who is taught 
thoroughly the Primary and Fundamental Rules,needs them not. 

In some books we find a still further division, as 

Single Eule of Three of Vulgar Fractions. 

Double Eule of Three of Yulgar Fractions. 

Single Rule of Three of Decimal Fractions. 

Double Rule of Three of Decimal Fractions. 

With equal propriety they might have added 

Simple Interest in Fractions. 

Compound Interest in Fractions. 

Discount in Fractions. 

Simple Interest in Decimals. 

Compound Interest in Decimals. 

Discount in Decimals, 
and so on, through the vocabulary of special rules with which 
our books abound. 

In other books we find rules enough for multiplying and 
dividing compound numbers to bewilder smy student, and 
which he makes no use of after he leaves the school room. — 
In some we find Tare and Trett, Commission, Brokage, In- 
surance, Assessments, Duties, Barter, Loss and Gain, &c, &c. 
But why stop ? Why not have rules for breakage, burnings, 
floods, school taxes, militia fines, State, county, road and poor 
taxes ? No wonder that pupils who have ciphered through the 
books, know nothing about arithmetic. 

If I were asked, what general rules I would adopt, I would 
say, Numeration, Addition, Subtraction, Multiplication, and 
Division : The extraction of the cube and square roots, and 
perhaps a few others. But I would never use a special rule 
where a general rule would answer. Proportion, or the Rule 
of Three,* I use as a general rule or guide to direct the stu- 
dent in his application of the primary rules. Strictly speak- 
ing, there are no general rules except the five primary rules 
first mentioned. Instead of teaching rules for different 

* But even these rules should be taught by the common sense of the 
pupil, rather than by the book. 



THE TEACHING OF AEITHMETIC. 61 

rates of interest, for years, for months, for weeks and for days, 
for discount, for commission, for gain and loss, per cent., &c, 
&c, in accordance with some of our test-books, I teach that 
per cent, is per hundred, and teach the pupil to apply the prin- 
ciple to practical questions. No special rule for per-centage is 
used and none is needed. Barter, Discount, (Single Position) 
Fellowship, &c, are but applications of the Eule of Three ;* 
and hindrances, in all cases. The pupil always learns more, 
and faster, without them. So with special rules, generally : 
the learning of them is worse than the waste of time. 

" It is interesting, amusing, and perhaps instructive to the 
pupil to compare the rule which he has arrived at by his own 
inductions, to the book rule : when he will often have the sa- 
tisfaction of seeing them the same.f When they differ, 
the Teacher may explain the difference. But, in no case, per- 
mit him to apply a rule to a practical question without a de- 
monstration :\ nor to perform any operation without a reason. 

* Or simple analysis. 

fin most cases the rules will agree ; but whether or not, let the rule 
be secondary to the principle, and not the principle to the rule. 

X We do not say that the pupil must (in all cases) be able to demon- 
strate, the operations of the square and cube roots of large numbers ; 
(or even long division) before he applies them to practical questions ; 
but that he should understand and be able to demonstrate their applica- 
tion and their principles. Never permit him to extract a root either of 
a large or small number, without a reason, or without understanding the 
principle : but the demonstrations of the operations on large numbers, 
may be postponed until the pupils mind is fit for it. In the No. 1 stage, 
these principles should be thoroughly taught on small numbers, by their 
application to practical questions ; before the pupil is able to perform 
the mechanical operations on large numbers. Roots of numbers as high 
as thousands, are easily solved without rules and as easily understood, by 
young children. The principles are easily demonstrated by 
diagrams on the black-board. Thus, the square of 3 is 9 : and 
the square root of 9 is 3. 

That the square of a fraction is less than itself, is 1 foo t 
readily demonstrated thus. Here is the square of a § 
linear unit : which is a square unit, or one square "" 

f00t - " TlboT 

Divide this square foot into four equal parts, thus : 
Each part will be half a foot long, and half a foot broad, M 
containing a quarter of a square foot. Thus the square of 
§ is plainly demonstrated to be %, so that when the pupil £| 
performs the operation %X%={, he fully understands it. — 
Cubes can be demonstrated t»y blocks, or cutting and apple. 



§TXl=l, 
i i 



12 1 



62 THE TEACHING OF ARITHMETIC. 

Although the pupil should not be allowed to pass over a prin- 
ciple without understanding it ; and when he is discovered to 
have passed over some essential principle without understand- 
ing it, he should be put back to it. Yet we do not pretend 
that he must be a thorough arithmetician before he can be pro- 
fitably put into algebra or geometry* If he thoroughly un- 
derstand the fundamental principles of arithmetic, although 
he may not be an adept in its practical application, he may be 
successfully taught algebra and mensuration.f But by no 
means would I abandon his former studies. Frequent reviews 
are beneficial. When the pupil becomes weary of a particular 
study, it is in vain that you endeavor to force him through ; 
but by advancing him, you encourage him ; and by frequent 
reviews on the blackboard you can perfect him in his former 
studies. As said in the last chapter, the advancing of a child 
in spelling before he has fully learned his alphabet, encour- 
ages him, and the letters themselves are taught thereby. So 
he may learn arithmetic by his progress in algebra. 

He may sometimes be placed as a Teacher of a class in arith- 
metic, which he will be ashamed as an algebra scholar to not 

be able to teach : and self respect will urge him to study him- 
self. 

To teach correctly, the Teacher himself should understand 
what he professes to teach. Not to be able merely to solve 
the question, but to demonstrate it; not to show his skill in 
ciphering, but to be ready at all times, in season, or out of 
season. "It is not enough," says Mr. Colburn, "that the 
Teacher is able, in some way, to obtain the answers to the 
questions. He should be able to give the reason for every 
step he takes in the process ; and in a clear and concise man- 
ner." If he do this, the pupil will soon be able to do the same. 

Every operation of the pupil should undergo the strictest scru- 
tiny. 

* Even a child can learn the elements of Geometry : and arithmetic 
can be illustrated by the elements of Algebra. 

t The pupil, however, should not be permitted to proceed with anything 
which depends on a former forgotten principle until he is again made 

"iTiAintpH with it. 



THE TEACHING OF ARITHMETIC. 63 

It is not even enough that he obtains the proper result know- 
ing it to be correct, unless he can explain the process step by 
step, and demonstrate its truth. If performed by a written 
rule, he must explain the rule. He must know the rule itself 
to be right. To require a child to commit a rule to memory 
which he does not understand, is absurd. How much more 
absurd is it to expect him to remember more than fifty rules 
which he does not comprehend, and apply them to practical 
use. 

Some Teachers discard all but the five primary rules. In 
my experience I have always found it necessary to teach a few 
other general rules : although, I believe, that most of them 
might be easily dispensed with. To depend altogether upon 
analysis, seems to leave the pupil too much without a guide,* 
while, too many, distract the mind and divert it from the true 
course. 

Every successful Teacher will agree with Mr. Colburn, that 
" Whatever you are teaching, keep this precept in view : Teach 
but one thing at a time, and apply yourself strictly to that, 
until the pupil is master of it, before he is put to another. Be 
sure that one thing be learned, before another is attempted.' 
Suppose that 9 cwt. 1 qr. 13 lbs. of sugar are to be mul- 
plied by 6. The pupil can multiply these numbers by 
6, but he needs to be told that they are to be multipli- 
plied ; he has not yet been sufficiently trained to think : Put him 
back to No. 1, and let his faculties be developed on simpler 
questions. Suppose he cannot multiply or divide compound 

* A pupil sometimes becomes embarrassed in a simple solution and docs 
not know how to proceed; when, by referring to some general rule, he is im- 
mediately put on the right track. For example, he wishes to obtain the 
price per gallon, when 31^ gallons are worth 20 dollars, and he hesitates. 
He knows that one number is to be divided by the other, but is at loss to 
tell which is the number to be divided. True, it is a plain question ; but 
the child is embarrassed ; by a simple statement of the Rule of Three, he 
is relieved, Sometimes a solution in Reduction is assisted thus ; if one 
yard contain 3 feet how many yards do 150 feet contain. 



64 THE TEACHING OF ARITHMETIC. 

numbers, teach him to do it (better by his own induction) than 
by the written rules * 

Suppose it is required to be reduced to a lower denomina- 
tion, and the pupil fails to do it, put him to Reduction. There 
may be a fraction as £ of a lb. to be reduced to the fraction of 
a cwt. Discover the point of failure. If in Reduction, put 
him back to it ; if in Multiplication or Division of fractions, 
put him there : but on no account refer him to such rules as 
<' multiply the denominator by the number contained in one 
of the next higher denomination." " But, it is much the best 
way, to teach him thoroughly as he goes." Teach him to 
think from the first. Let him do nothing without a reason. 
Require him to say not only how but why. 

The Teacher, is often annoyed by the pupil in mathematics 
during his attendance on other studies. How is this to be 
avoided? For the pupils in mathematics, especially the 
younger pupils in arithemetic to be busy only during the 
regular recitations, is a waste of time, which should not be 
permitted. To spend the interim wholly in preparing for the 
regular recitations, is also a waste of time. The study of their 
books, seems best adapted to that time. And here is wherein 
books may be made valuable assistants to the Teacher. He 
must not be annoyed during the other recitations; neither 
must the pupils at their seats, be idle. 

Henry K. Oliver, of Massachusetts, says : 

" It is a most lamentable fact, that in all of our common 
schools, there is (not because of any fault of the Teacher, but 
from the defects of the system,) a most profuse and shameful 
waste of time. A great portion of the customary school hours 
is wasted in absolute idleness, wasting the priceless energies 
of mind and body, to which any employment, even the most 
unsatisfactory, is preferable. 

* I once visited a School during a visit of the School Directors. A 
boy brought a solution to one of the Directors. He had multiplied 2£. 
3s. 6d. by 20, and multiplied it correctly too. " You should always go by 
the rule," said the Director (who had been a SchoolTeacher) "which says 
multiply by two or more factors, when the multiplier exceeds twelve." 



THE TEACHING OF ARITHMETIC. 65 

Some Teachers, to avoid this waste of time, examine all the 
slates that are presented to them during the other exercises. 
This is wrong. To permit idleness is also wrong. Some Teach- 
ers, in their eagerness to reform these abuses, discard text-books 
altogether. There does, indeed, seem to be no need for text- 
books, if the pupils are not permitted to use them, except at 
recitation ; for then, the Teacher, and not the book, should be 
the instructor. But the Teacher cannot, by any process, eith- 
er by writing the questions himself, or by giving them out 
orally to the school, prevent much waste of time. Some will 
have the question performed, before the others have begun. — 
Besides, the Teacher is thus interrupted in his attention to 
the regular recitations. A book, therefore, seems necessary 
to keep the pupils busy during this time. But let them be 
merely assistants. The Teacher himself, must be the principal. 
For a pupil to sit at his seat in the old way, performing cer- 
tain operations, and obtaining certain answers, without under- 
standing either the operation or the answer, is time worse 
than thrown away. Every operation should be explained by 
the pupil ; who may note down the explanations needed : to 
be given at stated times, either singly, or on the blackboard 
to the class, or to the whole school. It may be said that some 
may take advantage of this regulation to be idle. But he 
who is disposed to be idle, will no more trouble the Teacher 
with his slate, than be employed at his seat. It may be said 
by some who discard text-books that the pupil will learn to 
work, without principle, merely by the book. If from the 
first, he be taught aright, and to expect a rigid examination, 
he will work understandingly ; for he will expect to give a 
reason for what he has done. Besides, if taught aright, he 
will need but little assistance. 

This is also true with other studies : Natural Philosophy, 
Chemistry, Physiology, &c, &c. Let the oral explanations 
of the Teacher be thorough (and made interesting by 
amusing illustrations in anecdote, and interesting stories,) 
and they will be impressed upon the minds of the pu- 



66 THE TEACHING OF ARITHMETIC. 

pils. Whereas, by committing the lesson in the book to me- 
mory, they may learn nothing but the words. The Teacher 
should, in every study, prepare the pupil for the book, by oral 
explanations : when to read the book is sufficient. Nothing 
is gained by committing it to memory : and so every Teacher 
will experience who has tried it. 

In teaching arithmetic, the pupils should be taught system 
in their demonstrations. For example, I give out the ques- 
tion : If I give away \, |> and \ of my money, and have six 
dollars remaining, what had I at first ? The pupil performs 
the operation. 

" Will you explain it ?" says the Teacher. 

Pupil commences: "I multiply each numerator by" 

" Stop," says the Teacher, " that is the rule for obtaining 
the common denominator." 

Another pupil : " I first bring them to a common denomi- 
nator : then" 

" That," interrupts the Teacher, " is the rule for adding 
fractions : We wish the demonstration of this question.' ' 

Third pupil : "I add the fractions together, which makes 
f, the part of the money I gave away, — being f : consequent- 
ly the six dollars is | of the money I had at first, and the 
whole sum 24 dollars." 

He, or some of the others may, if necessary, prove the ope- 
ration ; or they may now demonstrate the adding process. — 
Suppose one of the class be requested to do so. 

He commences : " I multiply the numerator by" ■ 

"I have told you before," says the Teacher, "that is the 
rule for obtaining the common denominator." 

Another pupil : "I first obtain the common denominator; 
then add the numerators," &c. 

" That is correct," says the Teacher, " you may now explain 
the process of obtaining the common denominator — which is 
done by the pupil. 

But he should first be taught to obtain the common denom- 
inator by his own inductions, without reference to rule. Thus, 



THE TEACHING OF ARITHMETIC. 67 

J, \, and \ are equivalent to T \, 7 \, and 7 \ which added to- 
gether make / s — f ; which operation, the pupil can under- 
stanch 

Suppose the question to be — If three yards of cloth cost 
six dollars a yard, and I gain six per cent, by the sale of it, 
what was the selling price ? A pupil solves the question. 

T— " Will you demonstrate it ?" 

P. — " First I multiplied three by six to obtain the cost of 
the cloth ; I then multiplied by 6 (the rate per cent.) and divid- 
ed the product by 100 to obtain the gain, which I added to 18 
dollars (the cost,) which gives the answer." 

Now, this, although a thorough and complete demonstration, 
is wrong. The simple explanation should be, — I add $1.28 
(which is the 6 per cent, gained) to the cost ; which gives the 
required result. The Teacher, may, (if he think necessary,) 
question the pupils on the different parts of the solution ; as 
How did you obtain 6 per cent ? &c., &c. 

As before said, the Teachers' judgment must be his guide, 
respecting rules. Let us consider ! Shall we have merely a 
rule for Proportion, or Rule of Three, or shall we divide it into 
special rules for special subjects, one for Barter, and another 
for Loss and Gain, one for Supposition (subdivided into Posi- 
tion and Discount) one for Fellowship, &c, &c. ? Shall we divide 
it still further, into a rule for corn, and another for potatoes 
one for dry goods, one for groceries, and another for liquors ? 
Shall we discard proportion entirely, and depend on analysis? 
Shall we teach the pupil Addition and Subtraction, so that he is 
able to apply them to special cases, or divide them into rules, for 
subtracting the tare from the gross, for subtracting the loss, and 
adding the gain ? It seems evident* that too many rules per- 
plex the learner, while some seem necessary to afford a rest- 
ing place for the mind. 

I will now give you a short description of my system of 
teaching, not in a spirit of vanity, or dictation, but with the 

* The thorough teaching of the five primary rules are always under- 
stood as indispensable. 
5 



68 THE TEACHING OF ARITHMETIC. 

hope of contributing something useful to my fellow Teachers 
of Pennsylvania. My motto is — The fewer the rules, the bet- 
ter Arithmetic is taught. Ay, and the more speedily ; and, 
(what in this age is of importance) so as to stand an examination. 
The time is come when a book examination is of no avail. 

NUMBER 1, OR FIRST GRADE. 

This branch of teaching depending neither on the scholastic 
attainments of the Teacher, nor on any rules whatever, but al- 
together upon his ability to impart knowledge to children, is 
more appropriately the province of a class book than an edu- 
cational work. Yet a single example of this kind of practical 
exercises may not be amiss. 

A pupil who has never read a definition, or studied a rule, 
is asked to solve the following question : 

A man buys 9i yds of cloth at 7£ dollars a yard, and sells 
it for 2 dollars a qr. ; does he gain or lose ? how much ? and 
how much per cent ?* 

Solution: The price of nine yards, at 7| dollars, is 66£ dol- 
lars. 

The price of a quarter of a yard, at the same price is 7£ qrs. 
=3f halves=l| Dollars=$1.87£ : which, being added to $G6. 
50, make, $68,371. 

Nine yards and a quarter=37 quarters at 2 dollars a quar- 
ter, are sold for 74 dollars ; consequently there is a gain of 
$5,621. 

$5,621 are gained on 68.37i, — or 11.25 on 136.75,— which 
is 45 on 547, or 8H f per hundred. 

The explanation is simply — The cloth cost $68,371;, and ivas 
sold for $74 ; making a gain of $5,621 on $68.371 ; which is 
$8. 226+per hundred or per cent. 

Here is another example less complex : 

" A post is £ of its length in the mud, \ in the water, and 
10 feet above the water, what is its length ?" 

Solution : l+^= = S == J in the mud and water, consequently \ 
=10 feet, and the whole=20 feet. 

* Questions involving smaller numbers may be solved mentally. 



THE TEACHING OF ARITHMETIC. 69 

NO. 2 * 

The rules of Addition, Subtraction, Multiplication and Di- 
vision, with numeration, f and their application to practical ques- 
tions whether in Loss and Gain, Reduction, Interest or any- 
other rule of the book, the pupil is now expected to be made 
thoroughly acquainted with ; and, as he advances, their appli- 
cation to symbols as x+x+x+x—^x, x— sc=0, xXx == x z 1 &c. — 
This last exercise improves his analytical powers. 

Reduction is an important branch of arithmetic ; yet needs 
no special rules : and the pupil is practised in it, by every vari- 
ety of examples until he thoroughly understands it. 

I now take up Vulgar Fractions ; and teach, thoroughly, 
their primary rules. But I again repeat that I never refer a 
pupil to an abstract rule, for the solution of a practical ques- 
tion, until he has learned to do it by his own inductions. De- 
monstrate the principle not by the rule ; but the rule by the 
principle. I give the pupil no rule — either written or verbal? 
until his own mind, (assisted, if necessary,) by the Teacher, 
solves the difficulty, after which, a rule may be given to ex- 
plain, or enforce his inductions ; which is much better than to 
first give a rule which he does not understand, and afterwards 
explain it by demonstration. 

For example : I am teaching Addition or Subtraction of 
Fractions. 

The example is — Add together £ and £. The pupil will 
probably answer f ; but how he obtained the result, he cannot 
tell. I then ask — what is the sum of J and \ ? or \ and t ? — 
and he is at a stand. I then explain the first question, by 
changing the fractions to fourths, the sum of which is three, 
fourths. The pupil now understands that to add fractions to- 
gether, they must be brought to the same denomination ; and 
\ and h, — or f and £ — are shown to be equivalent to rV and t 4 z 

* Nos. 1 and 2 are somewhat similar to mental and written arithmetic. 

f The limits of this work will not permit the various methods of dem- 
onstrating these rules. Most Teachers, however, we presume, demonstrate 
them in their own way. 



70 THE TEACHING OF AEITHMETIC. 

— or I and ^. The pupil may then read the rule in the book, 
which he, himself, has made. 

In the study of Grammar, arbitrary rules must be sometimes 
learned; but in arithmetic, they should not be learned 
unconnected with principle. 

I once invited a visitor, to examine my pupils. After they 
had solved several questions, and denned a number of terms, 
(such as fraction, compound fraction, mixed number, &c.,) he 
asked, " What is an improper fraction?" 

" This is an improper fraction," was the reply, the boy 
chalking f on the black-board. 

" But what is the definition of an improper fraction ?" con- 
tinued the visitor. 

" A fraction greater than the whole." 

Knowing my visitor wished the book answer, I thus dreio 
it out. " What form is necessary for an improper fraction ?" 

Now, said I, Let me be the scholar, and you the Teacher. — 
Will you explain to me, what is an improper fraction ? 

A. — A fraction not proper. 

Why is it not proper? I asked. 

Because a fraction is a part, and an improper fraction is 
more than the whole. 

"Very good, I replied, but you are the Teacher, how will I 
write down an improper fraction ? 

Write the numerator greater than the denominator. 

I did so. Is that an improper fraction ? 

Yes, sir. 

But what kind of a fraction is this ? I continued, writing 
down 11. 

Improper, was the answer. 

But the numerator is not greater than the denominator. 

If the numerator is not less than the denominator, it is an 
improper fraction, he answered, without a moment's hesitation. 

Why is it improper ? I asked. 

For the same reason, the other is, he answered ; it is not a 
part of any thing ; being equal to the whole. 



THE TEACHING OF ARITHMETIC. 71 

These were the answers of pupils, averaging 10 years 
old, who were unacquainted with a written definition 

Decimal fractions are next taught, and their relation to vul- 
gar fractions, by practical examples. 

Proportion (or Rule of Three) I teach by practical examples, 
involving all kinds of numbers, simple, compound, fractional, 
and decimal. Such rules as Rule of Three in fractions, Reduc- 
tion of Fractions, &c, are discarded. The pupil who under- 
stands Reduction; and cannot apply it to fractions and deci- 
mals, has but partly learned it, unless he is deficient in the 
primary rules of fractions themselves. In either case, I turn 
him hack to the weak point ; but, in no case teach him by re- 
ference. Keep him at the weak point until he has learned it ; 
before he attempts to proceed further. 

I frequently give them questions in "Fellowship," "Dis- 
count," &c, &c, and after they are solved, refer them to the 
special rules in the book, and compare them with his work. — 
If the rules are useful at all, they are only so, when thus illus- 
trated ; when they may be pleasing and instructive. 

I next take up Interest ; and carry oat the principle of per 
centage. AsikeRuleof Three is so readily applied to questions 
involving Interest, I frequently use it as a medium of instruc 
tion. The pupil is expected, however, to be acquainted with 
the principle of per centage before entering into No. 2. 

In many of our books, there are Geometrical questions un- 
der special rules ; but as no pupil should meddle with Geo- 
metrical solutions, until he is acquainted with the elements of 
Geometry, they will be included under their proper head, — 
the teaching of Geometry. 

The rules for allegation, and progression, are good enough ; 
but like many other rules, of little importance. Their solu- 
tions belong rather to general arithmetic, than to special rules. 

As to " Double Position," it appears to be a rule entirely 
useless ; and besides, wholly incomprehensible to the young 
student ; who must depend altogether on the book, or the 
teacher, to know the truth, after he has obtained the result, 



72 THE TEACHING OF AEITHMETIC. 

by a rule which he cannot understand. True, he may prove 
it by analysis. So he may, without the supposition; and 
have the satisfaction of understanding his work. If he cannot 
analyze it, it is because he cannot understand it ; — neither can 
he understand the rule. 

Questions, in "Single Position," although a branch of the 
"Kule of Three," under which I teach it, when taught at all, ad- 
mit of beautiful analytical solutions. Examples : if I take a 
bag of corn to the mill, and fetch home 2 bushels, tV being 
deducted for toll, how much corn did I take to the mill. 

Solution: if T V be deducted, , 9 - are left. If ft = 2, what is 
one tenth : and what is the whole ? 

Example : if I sell goods for 6Q dollars, and gain 20 per 
cent, what was the cost ? 

Solution: as A of the cost is gained, consequently 66 dollars 
is H, and 6 dollars tV, and the cost, 60 dollars. 

Example, if by selling a knife for 10 cents, I have 20 per 
cent., what was the cost ? 

Solution: as he losses /A = i, 10 cents is I of the cost, 21 
i, and the whole cost is 12i cents. 

Or, as 10 is the £ of 80, which is 20 lost on 100, so £ of 
100 = 12£, is the cost of the knife. 

Many other rules are packed in a few pages, in some of our 
text books, amongst which we find " Annuities," " Combina. 
tion," "Permutation," "Duodecimals," &c, &c, which need no 
special rules. The pupil who cannot work Duodecimals with- 
out a special rule, should be taught " Compound Multiplica- 
tion." 

In conclusion, I quote another passage from Mr. Colburn, 
and recommend it to the attention of all teachers. 

" Eecitations should be conducted briskly and not suffered 
to lag, and become dull. The attention of every scholar should 
be kept on the subject, if possible, so that all shall hear every 
thing that is said. For this, it is necessary that the ques- 
tions pass round quickly; and that no scholar be allowed a 
longer time to think than is absolutely necessary. 



THE TEACHING OF ARITHMETIC. 73 

"There is one point more that I shall urge ; and it is one 
which I consider the most important of all. It is to make 
the scholars study. I can give no directions how to do it. — 
Each teacher must do it in his own way, if he does it at all. 
He who succeeds in making his scholars study, will make 
them learn; whether he does it by punishing or hiring; 
or persuading, or by exciting emulation, or by making 
the studies so interesting that they do it for the love of it. — - 
It is useless for me to say which will produce the best effects : 
You may judge of that for yourselves. But this, I say, that 
he who makes his scholars study, will make them learn ; and 
he who does not, will not make them learn much, or well." 

PRACTICAL EXAMPLES OF THE SCHOOL-ROOM, ILLUSTRATING 
THE METHOD OF TEACHING. 

I cannot close this Chapter, without giving a few examples 
in the experience of the practical teacher. 

The juvenile class in the arithmetical tables. 

Teacher — How many quarters in four yards ? 

Not known. 

T. — How many quarters in one yard ? 

P.— Four. 

T. — How many in two yards ? 

P.— Eight. 

So proceed to three yards ; to four yards, &c. 

T. — How many yards in sixteen quarters f 

P. — Sixty -four. 

T.— Why? 

P. — Because four quarters are in one yard ; and four times 
sixteen are sixty-four. 

T. — How many yards in four quarters ? 

A. — After a pause — one. 

T. — How many in eight quarters ? 

A.— Two. 

T. — In sixteen quarters ? 

A. — Four. 

T. — How did you obtain four ? 



74 THE TEACHING OF ARITHMETIC. 

A. — By dividing by four, the number of quarters in a yard. 
T. — Your first answer to this question was 64, now it is 4 : 
which is right ? and for what reason ? 

DEMONSTRATION" OF THE "RULE OF THREE," TO A CLASS OF PU- 
PILS FROM SIX TO EIGHT YEARS OLD. 

T. — If one slate cost 2 cents, what will 25 slates cost ? 

Place the same name as the answer in the third term. What 
is the answer to be ? slates or money. 

A. — Money. 

T. — Is the answer to be greater, or less than this third term? 

No answer. 

T. — What is the answer to be ? (repeats the question.) The 
answer is to be the price of what ? 

P. — Of twenty-five slates. 

T. — What is the third term, the price of? 

P. — Of one slate. 

T. — Is the answer to be greater or less than the price of one 
slate ? 

P. — Greater. 
. T. — Is the answer to be greater or less than this term ? 

P. — Greater. 

T. — Then place the greater of the remaining two terms for 
the second term. 

A few similar questions will imprint the rule upon their 
minds better than committing it to memory : and besides? 
they will understand it. 

PER CENTAGE. 

T. — I bought cloth for 80 cents a yard, and sold it for 90 
cents a yard, what is the gain per cent ? 

Explanation : T. — If I gain 10 cents on 90 cents, what do 
I gain on a hundred cents ? By the Eule of Three, what is 
the 3d term to be ? 

P.— Gain. 

T. — Is the answer to be greater or less than the third 
term, &c. 



THE TEACHING OF ARITHMETIC. 75 

Another mode: "I gain i§, or i of thecost. £ of 100 = 12z 
or 12? per cent." 

QUESTIONS TO MAKE PUPILS THINK. 

Bought 4 knives for 20 cents a piece, and 12 forks for a 
dollar, what is the price of one fork ? 

If I buy 40 bushels of oats at 50 cents per bushel, and sell 
them for 60 cents a bushel, and by so doing gain 20 percent., 
how many cents a bushel do I gain ? 

James can run 50 rods a minute, and John can run I of that 
distance in the same time, how many miles an hour can James 
run ? 

From Smith's Arithmetic. — "A merchant bought 26 hos:s- 
heads of wine at $2.00 a gallon, on 6 months' credit ; but by 
paying cash, he got it five dollars a hogshead cheaper ; how 
much did he save by paying ready money ?" 

PROMISCUOUS EXAMPLES. 

Eeduce f of a shilling to £ : or (as the book says) " to the 
fraction of a pound." 

A pupil solves it by some book rule : the Teacher requests 
him to explain. 

P. — I multiply the denominator by — 

Stop, said the Teacher, I think, to reduce shillings to pounds, 
you divide by 20. James, can you do it? said the Teacher. 

James does it, and demonstrates it thus — I divided by 20. 

Right, said the Teacher. 

But, said the first pupil, mine is done the same way. 

You told me that you multiplied, continued the Teacher. 

Well, persisted the pupil, did not James multiply. 

James, asked the Teacher, did you multiply ? 

No, sir, replied James, I divided. 

And how did you divide it ? 

I multiplied the denominator by the divisor. 

Now, William, said the Teacher, addressing the first pupil, 
Here is the difference in your solutions. You multiplied by 20, 
as you would have multiplied the same fraction, had you been 



76 THE TEACHING OF ARITHMETIC. 

required to multiply f by 20, and thought you had multiplied : 
whereas you actually divided by 20, without knowing it ; and 
by so doing obtained the correct result. James knowingly di- 
vided according to the principles of Eeduction, and obtained 
the same result. James understands Eeduction, and knows 
how to divide fractions : you — neither. He knows he is cor- 
rect ; because he understands his work : you do not, because 
your work is taken from a book or Teacher, and is not under- 
stood. 

MENTAL EXERCISE. 

"If I sell an article for $100, and gain 10 per cent, what 
did it cost ?" 

A pupil solves it thus: " 100 — 10 = 90 dollars, the cost." 

I then write down " bought for sold for " and 

ask him to fill the blanks; which he did, thus: "bought for 
90, sold for 100." 

"To gain 10 per cent, what must I sell it for?" asked the 
Teacher. 

Pupil. — " One hundred dollars." 

" How much did I gain ?" continued the Teacher. 

" Ten dollars," was the reply. 

I gained 10 dollars on — what ? 

On ninety dollars. 

Is the gain of 10 dollars on 90, a gain of 10 per cent.? 

No, sir, it is more than 10 per cent. 

To really gain 10 per cent, on $90, what must he sell it for? 

The pupil calculates it, and answers — " Ninety -nine dollars." 

Then, if I sell for 100 dollars, and gain 10 dollars, I gain 
more than 10 per cent. 

Yes, sir. 

Your error then, is in calculating the per centage on the 
selling price instead of the buying price. 

Yes, sir. 

And, if I sell goods for $99 dollars, and gain 10 per cent., 
what did they cost ? 

Ninety dollars. 



THE TEACHING OF ARITHMETIC. 77 

How did you obtain ninety ? 

By substracting nine, the ten per cent, gained, from the selling 
price. 

Where did you get the 9 dollars ? 

Ten per cent, on ninety. 

But you have not the ninety to work with : and to subtract 
10 per cent, from 99, as you did from the hundred, would not 
leave ten dollars. In the former case, you subtract 10 per cent, 
of the selling price, now you subtract 10 per cent, of the buying 
price. Now, we will return to the first question. 100 dollars 
is the selling price : I have gained 10 per cent, on what ? the 
buying price, or selling price ? 

The buying price ? 

But you have taken it from the selling price, and made 90 
dollars, the buying price, upon which, according to the question, 
you gain 10 per cent, which amounts to 99 dollars : not a hun- 
dred. But, leaving the first question, and taking up the last : 
99 is the selling price, he has gained 10 per cent, what is the cost? 
We know it to be 90 ; but 10 per cent, of 99 subtracted from 
it, will not be 90 ; neither is 10 per cent, of 99, to be sub- 
tracted; but 10 per cent, of 90, to be subtracted from 99. But 
you have no right to the 90 ; that is the number to be found : 
and, in the first question, you have not the buying price, and 
consequently cannot use it. Now, how are you to obtain the 
10 per cent, on a number, which you have not? 

The pupil is at a stand. His curiosity is awakened. 

" Well," continued the Teacher, "you are at a loss to know 
how to obtain the per centage of an unknown quantity. Mark 
this : an unknown quantity. Suppose a number." 

" What number will I suppose ?" asked the pupil. 

"Any number. A hundred is an easy number for per 
centage calculations: but any other number will answer. — 
Take $50. That is, suppose fifty dollars to be the buying 
price. Now if you gain 10 per cent, what is the selling price ? 
Work with the supposed number, as if it were the true one." 

The pupil works it, and makes the selling price fifty-five 
dollars. 



78 THE TEACHING OF ARITHMETIC. 

" Now," I continued, " here is a plain question of the ' Eule 
of Three.' If, when 50 is the cost price and 55 the selling 
price, I gain 10 per cent, what must be the cost, to gain the 
same per cent, when the selling price is $99, or $100, or any- 
other number?" 

The pupil states it on the slate, according to the rule, thus : 

Selling price. Selling price. Cost. Cost. 

$55 : $99 : : $50 : $90 
$55 : 100 : : $50 : 90 tf $90.90 tf. 
This is the pupil's first idea of "Position," or "Discount." 

Such questions, however, as before stated are mostly solved by 

analysis. 

EXERCISES ON SLATE : 

" Multiply ,V ¥ by 38." 

The pupil could not work this example : because he could 
riot understand it. 

I simplified it. 

Multiply i by 2, i X 2. He still could not do it. 

I simplified it further. Multiply £ by 2, i X2. "How 
much is two halves ?" 

Answer — " One." 

" How did you obtain the one ?" 

" I know that two halves are one." Here was the end of 
his explanation. Here was a starting point. 

" How many apples are two times one apple ?" Thus, 

1 X 2 ^how many ? 

apple 

Ans.— " Two." 
" Two— what ?" 
"Two apples." 
1 x 2 = J_ h X 2 = what? _J_ . Let this principle be 

apple third apples 

carried out in numbers. 

Ans.— "Two thirds, §." 
_!_, £ x 2 = what ?" 

half 

Ans. — "Two halves, I = 1." 
Five multiplied by 2, I + 2 = what ? 

sixths 



THE TEACHING OF ARITHMETIC. 79 

Ans. — Ten sixths. V. 

Twenty-nine, seven hundred and thirty-fourths, multiplied 
by two, ih X 2 = 7 3? : and upon the same principle proceed 
until the pupil understands the first question, W* X 38, when 
he will find no difficulty in doing it. If, when he obtains the 
result, which will be an improper fraction, he cannot change 
it to its proper terms, (as was the case in this example) turn 
him back, and keep him there, until he fully understands an 
improper fraction. 

" What number is that which being multiplied by 15, will 
make f ?" 

It is not understood, and I chalk on the black-board — 
15+ = f. 

It is now understood : but the principles are not sufficiently 
clear. I chalk immediately under the former, 8 X =16, 
and they all cry out — " Two." 

" Where do you get the two V 

"Eight two's are 16." 

I change it again, "15 X = 210." Thus I proceed until 
the principles of multiplication and division are understood, 
as applied in these questions. 

"But," says one, "§ cannot be divided by 15." 

The principle is now understood, but not division of frac- 
tions. This is the weak point ; and the pupil must apply him- 
self to that until he is master of it. 

"What number is that which being divided by 15, will 
make & ?" 

Illustration : 15) -j- m 15Vi" : and proceed as in the for- 
mer example. 

I once visited a school, some of the pupils of which had 
been through Davies, /Smith and Emerson. I gave them the 
following question : 

"If 4£ yards of cloth which cost \ of £ of 6 J dollars, are 
to be lined with muslin of the same width, at a cent a yard, 
what is the cost of the muslin?" 

In the solution of this question, there is nothing to do, but 



80 THE TEACHING OF ARITHMETIC. 

to think ? When it is understood, it is done. A pupil 
should be taught to think, as well as to understand. 
If every question is so simplified, that it requires no mental 
labor to understand it, the pupil will not soon learn to think 
himself. 

It is probable that most of the pupils could have solved this 
question had they taken the trouble to think ; or had they 
been furnished with a slate and pencil. But they were re- 
quired to do it mentally : and they failed. 

In a school which I once visited, I witnessed the following 
exercise. 

First Class in Arithmetic* 

"If a man buy goods for twenty dollars, and sells them for 
twenty-five dollars, what will be the gain per cent ? 

The question was solved immediately, by one of the class : 
a small boy. 

,' How did you do it ?" asked the Teacher. 

" I made a fraction." 

"How did you do it?" asked the Teacher. 

" I made a fraction, by writing the gain or loss for a numer- 
ator, and the cost for the denominator ; then changed it to a 
decimal." 

« Why did you do it in this manner ?" continued the teacher. 

" Because the rule says so," answered the boy. 

I give this example, to compare it with the manner in which 
some of us old Fogies were taught, and also with the newer 
mode. Most of us remember when all that was required of a 
pupil in arithmetic, was, for him to do the question and show 
it to the Teacher. No explanation was required, and none 
given. I allude to those termed good schools, where rules were 
committed to memory. We have also seen schools where noth- 
ing was required but, " Master, it brings the answer," let the 
operation be right or wrong. 

The comparison with such schools was favorable. 

" I never permit my scholars," said this Teacher, " to do a 

* Pennsylvania School Journal. 



THE TEACHING OF ARITHMETIC. 81 

question without repeating the rule by which it is done. — 
They must know the rule by heart, before I permit them to 
begin the question. Every rule in the book," he continued, 
with emphasis, " must be committed to memory." 

I requested permission to ask a few questions i which was 
cheerfully granted. 

" Well, James," said I, " will you explain your question to 
me?" 

" Yes, sir," replied the boy. " I made a fraction by writing 
the gain or loss, for a numerator, and the cost for a denomina- 
tor ; then changed it to decimal." 

" Why did you make this fraction ?" 

" Because the rule says so." 

" But why does the rule say so V 

" Don't know." 

" I will now give you a question," I continued ; " I have 
four marbles : — if I give two away, how many will I have 
left?" 

" Two," immediately answered the boy. 

" How did you get the two V 

" I subtracted two from four." 

" Why did you subtract ?" 

(No reply.) 

" Did you subtract," said I, because the rule says so ?" 

"No, sir." 

" Let me do it for you," said I, taking the slate, and divi- 
ding four by two. " Is this right ?" 

11 No, sir," replied the boy, quickly. 

" But you see," said I, " that I have the same answer ?" 

" But," replied the little fellow, now becoming animated, 
" it isn't right for all." 

" Let me read this rule," said I, looking on the slate, " di- 
vide one number by the other and the result will be the an- 
swer." 

The little boy stared. 

" That rule is not here," I continued ; " but suppose that it 
were, would it be right?" 



82 THE TEACHING OP ARITHMETIC. 

" No, sir." 

" What reason can you give for thinking that it is not 
right ?" 

" I know it is not right" he answered with emphasis. 
" And do you know that this rule in the book is right ?" 
Pupil, hesitating, " It brings the answer." 
" So does my rule, dividing by two." 
" But, the master says mine is right." 
" So it is," said I, " your master is right. But would it 
not be better for you to know it to be right, without depend- 
ing on your master ? Wouldn't you like to know that your 
answer is right, without looking at your book, or asking your 
master?" 

" Yes sir, I would." 
" Well then, what is per cent ?" 
" Per hundred," was the reply. 

He had faithfully committed to memory all definitions. 
" Six per cent, then, means— what 1 Six dollars per hun- 
dred ]" 
" Yes sir." 

"Six gained on every hundred." 
'•Yes, sir." 

" Well, then, what is the question. What did he gain by 
the sale of the goods. 

After some explanation the pupil answered — "Five dol- 
lars." 

" He gains five dollars on what, — the selling price, or buying 
price." 

This question was also answered, when fully understood. 

Well, I continued, what does your question ask. 

It asks what is the gain per cent, replied the boy. 

And what is per cent. 

Per hundred. 

If then, said I, he gains five dollars on twenty dollars, how 

much does he gain on fifty. Is that it. 

No, sir, on a hundred. 



THE TEACHING OF ARITHMETIC. 83 

Well then, I continued, if he gains five dollars on , I 

paused and looked inquiringly. 

On twenty, answered the pupil. 

Well, then, if he gains five on twenty, what does he gain 
on a hundred. Is that it. 

Yes, sir. 

Very well, can't you answer that. If you gain five on 
twenty, how much is it on a hundred. 

After a short pause, the truth flashed on his mind, and he 
answered, Twenty-Jive. 

Are you sure you are right. 

Yes, sir. 

Why. Because it is the answer. 

No, sir, I know it is right. 

Because the rule says so. 

No sir. 

Because your Teacher says so. 

No, sir. 

How, then, do you know. 

i" know it, was the emphatic reply. 

Mark that, Fellow Teachers : he ejstew it. This boy's mind 
was "waking up. 

I did not question him further. Here was the first process 
of thinking ; and I would not confuse him with further ques- 
tions. 

We select the following examples from Page's " Theory 
and Practice of Teaching," which show that the " drawing out 
process," carried to an extreme, is as bad as the " pouring in 
process." 

Example 1st. — "John," says the Teacher, "what is the 
number to be divided, called?" 

John hesitates. 

" Is it the dividend ?" says the Teacher. 

" Yes, sir, the dividend." 

" Well, John, what is that which is left after dividing, call- 
ed ? The remainder — is it ?" 



84 THE TEACHING OF ARITHMETIC. 

"Yes, sir." 

A visitor now enters the room, and the Teacher desires to 
show off' John's talents. 

"Well, John, of what denomination is the remainder?" 

John looks upon the floor. 

" Isn't it always the same as the dividend, John ?" 

" Yes, sir." 

"Very well, John," says the Teacher, soothingly, "what 
denomination is this dividend ?" pointing to the work upon 
the board. " Dollars, is it not?" 

" Yes, sir, dollars." 

" Very well ; now what is the remainder?" 

John hesitates. 

" Why, dollars too, isn't ?" says the Teacher. 

"Oh yes, sir, dollars/" says John energetically, while the 
Teacher complacently looks at the visitor, to see if he has 
noticed how correctly John has answered. 

Example 2d. — Class in " Colburn's First Lessons." 

" Where do you begin ?" said the Teacher, taking the book. 

Pupils. — " On the 80th page, 3d question." 

Teacher.— 11 Eead it, Charles." 

Charles, (Reads.) " A man being asked how many sheep 
he had, said that he had them in two pastures ; in one pasture 
he had eight ; that three fourths of these were just one- third 
of what he had in the other. How many sheep were there in 
the other?" 

T. — " Well, Charles, you must get the one-fourth of eight, 
must you not ?" 

G-" Yes, sir." 

T. — " Well, one-fourth of eight is two, isn't it?" 

G. — " Yes, sir, one-fourth of eight is two." 

T. — " Well then, three-fourths will be three times two, 
won't it f 

G.— a Yes, sir." 

T. — " Well, three times two are six, eh?" 

<7__« Yes, sir." 



THE TEACHING OF ARITHMETIC. 85 

T. — " Very well. (A pause.) Now the book says that this 
six is just one-third of what he had in the other pasture, don't 
it?" 

C— "Yes, sir." 

T. — " Then, if six is one-third, three thirds will be — three 
times six, won't it ?" 

a— "Yes, sir. 

T. — " And three times six are — eighteen, ain't it ?" 

0.—" Yes, sir." 

T. — " Then, he had eighteen sheep in the other pasture, had 
he?" 

C— "Yes, sir." 

T. — " Next, take the next one." 

At this point I interposed, and asked the Teacher if he 
would request Charles to go through it alone. 

" Oh, yes," said the Teacher, " Charles, you may do it 
again." 

Charles again read the question, and — looked up. 

" "Well," said the Teacher, " you must first get one-fourth of 
eight, musn't you?" 

" Yes, sir." 

"And one-fourth of eight is two, isn't it?" 

" Yes, sir." 

And so the process went on, till the final eighteen sheep 
were drawn out as before. 

The Teacher now looked round, with an air which seemed 
to say, " Now, I suppose you are satisfied." 

" Shall I ask Charles to do it again ?" said I. 

The Teacher assented. 

Charles again read the question, and — again looked up. 
I waited and he waited, but the Teacher could not wait. 

" Why, Charles," said he impatiently, " you want one-fourth 
of eight, don't you ?" 

" Yes, sir," said Charles, promptly ; and I thought best not 
to insist further at this time upon a repetition of a Yes, sir, 11 
and the class were allowed to proceed in their own way. 



86 THE TEACHING OF ARITHMETIC. 

These few examples are deemed sufficient to show the modes 
of teaching used in some of our schools. That they may be 
beneficial to Teachers, especially the inexperienced, is the wish 
of the compiler. 

Many more might be added, but these may serve to give an 
outline of the modus operandi of this branch of a common 
school education. 



CHAPTER V. 

THE TEACHING OF GEOGRAPHY. 

Elias Schneider, Superintendent of Public Schools at 
Pottsville, Pa., says in the Pa. School Journal : 

" The true method of teaching Geography is to present to 
the mind and imagination of- the pupil, a vivid and living rep- 
resentation of the geographical features of the earth, which 
will, as much as possible, take the place of the real and actu- 
al objects themselves." 

To do this successfully, it is necessary that the school-room 
be furnished with large and well delineated maps. 

For teaching Geography, we need not say that nothing is 
better than outline maps ; whether used in chanting, singing, 
or otherwise, every Teacher should judge for himself. 

But leaving this disputed point, the maps themselves are 
decidedly the best means for instruction in local geography. 

With the use of the outline maps in the school, none of the 
pupils can be ignorant of Geography. By having the map 
in the a mind's eye" he will also have impressed upon his 
mind, the figure of different parts of the Earth's surface : — the 
situations of towns, courses of rivers, &c, which these maps 
represent. 

Descriptive Geography is as easily taught as history, or 
any thing else descriptive. 

We know that such description as 

" The rocks along the south coast of France, are covered 
with a pretty hanging bush, with a large and delicate white 
blossom, having a number of fine purple filaments : — this is 
the caper bush," — (and in as plain and simple language as this, 



88 THE TEACHING OF GEOGRAPHY. 

can any description be given,) is interesting to children. So 
is the following: "The word archipelago means a sea full of 
islands. A great many currants grow in some of the islands 
of the Grecian Archipelago. They grow on low bushes, in 
bunches, like grapes." 

But a dull and prosy account of the imports and exports ; — 
or " Grenada, Seville and Cordova, were once Moorish Capitals; 
Malaga and Alicant export Wines and Fruits; Bilbao, Wool; 
and Santander, Grain and Flour. Valencia is noted for Silks ; 
Toledo for sword blades; Salamanca for its University ; and 
Alamaden for its Quicksilver,'''' is not interesting. The child 
who has a good verbal memory may remember the words so 
as to repeat them at recitation as a pupil of mine once answer- 
ed that " Commerce and Manufactures is the Governor of the 
State, and George Wolf the occupation of the people of 
Pennsylvania :" and not remember them until the next recita- 
tion; but he has learned nothing more than he who didnH 
know his lesson, because he could not remember words without 
meaning. 

Most children remember that the city of Venice is situated 
on 72 small islands, connected by upwards of 400 bridges, 
with canals for streets, boats for carriages, &c. ; and that 
Holland is so low a country, that embankments are built 
around it to prevent its being overflowed by the sea ; and the 
description of the Malstrom on the coast of Norway, and, of 
the Bay of Fundy, whose tides rise to the height of 60 feet, 
as described in our text books, and so they would any other 
description, if described in an equally interesting manner : 
and this the skillful Teacher can do. 

The way to teach description of any kind, is to make it 
interesting to the pupil : and the only difference in this re- 
spect, between descriptive Geography and History, is that the 
latter abounds in interesting incidents ; while the former is 
mostly dry, and uninteresting. Now, it seems to be the 
province of the Teacher to make it interesting. How is this 
to be done ? Let some interesting incident be related in con- 



THE TEACHING OF GEOGKAPHY. 89 

nexion with it ; and the pupil will readily remember it. We 
all know the eagerness of children to listen to stories. For 
instance, in describing a coal region, relate some entertaining 
anecdote, a visit to the mines, some ' hair-breadth ' escape of 
the miners, or any thing connected with them in a ' Peter 
Parley ' style : and if your pupils do not eagerly drink in your 
words, they are different from any children I ever saw. 

Mount Vesuvius, Etna, St. Helena, and many other places, 
have interesting historical incidents connected with them, 
which will impress them both historically and geographically 
upon the pupil's mind. In short, some striking event may be 
connected with every geographical description, whether of 
soil, climate, products or manufactures. If no real incident is 
in the Teacher's memory, his mind must be barren whose in- 
ventive faculty cannot supply the place of a real incident, by 
one of imagination : who cannot please children by an anec- 
dote : — being careful, however, to distinguish between the fic- 
titious and the real. Philosophy, Chemistry, Physiology, 
History, and Geography, abound in incidents, pleasing and 
instructive. The kite of Franklin, his electrical bells, and 
hundreds of amusing incidents connected with science, form a 
never-failing fund of instruction and delight, not only to the 
child, but to the more advanced pupil. 

" It is an excellent plan," says Mr. Page, "to keep a com- 
mon-place book of considerable size ; different portions of it 
being set apart for the different subjects upon which he is to 
give instruction. Under the heads of Geography, History, 
Arithmetic, Grammar, &c, &c, reserving quite a space for 
miscellaneous matter. Under these different heads, let him 
note down from time to time, such illustrations as he may hear 
of those respective sciences, anecdotes, incidents &c, &c, to be 
used from time to time in his school."* 

Thus we see that by means in the power of a Teacher, de- 

* Mr. John Beck, the Principal of the Litiz Academy, informed me 
that he had practised this mode for years, with success. The manner 
in which he relates his anecdotes to his pupils, in true Peter Parley style, 
always secures him attentive listeners. 



90 THE TEACHING OF GEOGRAPHY. 

scriptive Geography may be made a very interesting study. 
Of course, it is to be understood that as the pupil advances, 
he should be taught physical Geography : the nature of the 
zones, climate, motion of the earth &c, &c., but this part of 
the science is of itself so full of interest, that no Teacher who 
himself understands it, can fail to make it interesting to his 
pupils. 

I will close this Chapter by the opinions of a distinguished 
Teacher on this branch of teaching, James G. Carter. 

" While I hold my own opinion on this subject," says Mr. 
Carter, "and claim the right to state, to explain and to vindi- 
cate them ; if others hold different opinions, they have the 
same rights." 

With this apology, he proceeds : " The pupil, by some of 
the most approved systems, is presented in the onset with a 
map of the whole world, reduced to the size of a hat crown. 
In connexion with this, he is directed to read (and sometimes 
commit to memory) a description of the largest rivers, moun- 
tains and seas ; and also to learn some accounts of the charac- 
ter and manners of the principal nations. Perhaps he will 
soon be required to learn the amount of exports and imports, 
of the most commercial nations, to the accuracy of a farthing 

" Some, not content with presenting the whole earth, to the 
first and single glance of the young learner, and, as if deter- 
mined to push the absurdity of the plan to the utmost, have 
given the whole system to the child, for his first lesson in 
Geography. This is called setting up landmarks, and getting 
a general knowledge of the subject ; but, so far from that, in 
my view, it is getting no knowledge at all. It is only a con- 
fusion of words, without any definite meaning attached to them 
Avhatever. 

" The subject is begun precisely at the wrong end. If it is 
addressed to the understanding of the pupil, this arrangement 
seems to presume that he will take a deeper interest in, and 
better comprehend the general features of the world, embrac- 
ing the largest mountains and rivers, and the characters of 



THE TEACHING OF GEOGRAPHY. 91 

nations, of whose existence he has, perhaps, never before heard, 
than the roads, hills and rivers, of his own neighborhood, and 
the boundaries of his own township, county or State. Besides, 
upon the strictest philosophical principles, it is perfectly 
demonstrable that he can get no adequate idea of the magni- 
tude of the largest mountains and rivers of the world, except 
by comparing them with the mountains and rivers which he 
has seen ; and of which he has formed some definite idea. ' A 
river, three times as wide as our river.' This is the natural 
language of children ; and it is philosophical language. In 
forming a conception of a distant mountain Or river, which 
we have never seen, we proceed precisely as we do in forming 
a conception of any other magnitude. We fix upon some- 
thing of the same kind, which is known as a unit of measure • 
and then compare, and discover the relation of what is known 
with what is unknown. So the child, could form some idea 
of a mountain twice as high as a hill before his eyes ; or he 
could form a tolerable conception of a river three times as 
broad as the brook which runs before his father's door, or the 
river he may, perhaps, have seen in a neighboring township ; 
but talk to him at once of a mountain many thousand feet 
high, and a river a hundred miles wide, and I am much mis- 
taken if he forms the least conception of what he is told."* 

Singing and chanting the names and situations of places, I 
have found beneficial in impressing them on the memory : bu^ 
I do not contend for it. The only advantage gained by this 
mode is, that by a simultaneous recitation, the whole school 
is taught in less time than one pupil can be taught by other 
methods. It is a pleasing change ; and relieves the mind 
from the monotony of the school-room. Other exercises will 
also do this ; but as singing is admitted to be as effectual in re- 
laxing the mind, as any other exercise, if in connexion with 
this, the names of places, their situations, the capitals of 
countries, arithmetical tables, or any knowledge which de- 

* This is also the opinion of other distinguished Teachers, Schneider 
Page, and others. 



92 THE TEACHING OF GEOGEAPHY. 

pencls entirely on the memory is learned, it is an actual gain, 
admitting it to be not the best method of teaching. It may 
be that "the memory is not strengthened by such exercise:" 
but' it is certain, that pupils of six years old taught by it can 
answer more respecting local Geography than many Teachers 
are able to answer, so far as regards mere memory ; and further 
than that, no Teacher contends for ; and this is all many Pa- 
rents or Directors ask for. 

If this exercise be practised in connexion with outline 
maps, the situations of countries, and their towns, rivers, 
mountains, &c, will be impressed on the memory in much 
less time and with less labor than by any other method. 
We admit that this method is defective : but as it 
is merely a pleasing variety, in which the whole School is 
interested, unless it is an actual hindrance, no valid objections 
seems to be against it. The pupils all soon know their tables- 
capitals of every country in the world, and various other, 
items of knowledge, many of them, before they can read a 
word: and better too (so far a regards mere memory)"" than 
when taught by any other method. In fact, any thing that 
depends on the memory alone, can be taught to the whole 
school by the concert method, in less time than it can be taught 
to one pupil alone. I know that I differ with some experienced 
Teachers ; but if you have the maps, (or even atlases) the trial 
will cost neither you nor your pupils any thing but a pleasing 
and exhilerating exercise. 

Another very effectual method, and we might say one of 
the most effectual, as imprinting a " vivid and living represen- 
tation of the Geographical features of the earth," upon the 
pupil's mind, is the drawing of maps. Not only measured 
representations of portions of the earth's surface, but frequent 
chalk drawings on the black board. Those who practice this 
exercise, soon become able to delineate, with tolerable exact- 
ness, the outlines of States and Countries, their towns, rivers, 
mountains, &c, without having the map before them. 

In short, the Teacher who, himself, is well acquainted with 



THE TEACHING OF GEOGRAPHY. 93 

Geography, cannot fail to make it interesting to his pupils, if 
he tries ; and being interested in it, they will learn. But if he has 
to search the map himself, to assist the pupil in finding the 
location of towns, rivers, islands, capes, &c, it soon becomes 
a wearisome up-hill exercise to both Teacher and pupil. If 
the Teacher himself is acquainted with physical or descrip- 
tive Geography only as he looks over each day's lesson in the 
text book, how can he be interested in it himself, and how can he 
expect the pupils to be interested, or to learn. It is probably 
true, to a great extent, with those Teachers who fail in teach- 
ing any branch, that the Teacher himself, is deficient in knowl- 
edge. Although it by no means is a corrollary that all 
Teachers who have the requisite knowledge, are able to teach, 
without being acquainted with the art or science of teaching. 



CHAPTEE VI. 

THE TEACHING OF GEOMETRY AND ALGEBRA. 

My reason for including Geometry and Algebra in one 
chapter, is that he who can teach Arithmetic thoroughly, can- 
not fail in any mathematical branch he is acquainted with. — 
Yet, as the elements of Geometry and Algebra, are connected 
with mathematics in general, a few words on the teaching of 
them may not be unnecessary. As Algebra is but Arithmetic 
by symbols, if the pupil is acquainted with the principles of 
Arithmetic, he is already acquainted with the elements of 
Algebra. Algebra being pure analysis, rules seem to be 
almost unnecessary. There can be but one mode of teaching 
Geometry. If a pupil merely copies the figures from the 
book, he is not learning it. Mensuration, Surveying, &c, are 
but the practical application of the principles of Geometry. 

In teaching these branches, I lay down two general rules* 
of which all other rules are but modifications, viz: multiply 
the length by the breadth, to obtain an area, — and multiply 
the area of the end by the length to obtain the solidity. These 
rules are thoroughly explained. A triangle being demonstra- 
ted (by means of diagrams) to be half of a parallelogram of 
the same length and height, to calculate its area, needs no 
further rule. 

The mean length and breadth of a trapezoid is also easily 
demonstrated by a diagram. A trapezium or any irregular 
figure bounded by straight lines, is divided into triangles. — 
So with regular polygons. As the circumference of a circle 
is (in practical application) an infinite number of straight 
lines, it is the sum of the bases of an infinite number of 



THE TEACHING OF GEOMETRY AND ALGEBRA. 95 

triangles with the length of the radius for their perpendicular 
height : consequently the sum of the areas of the triangles, is 
the area of the circle. Solids are demonstrated by blocks or 
by dividing an apple or potato. 

F. J. Thayer says: "It is the peculiar property of Geometry, 
to be adapted to every capacity. Children of from six to ten 
years of age, may be as much benefitted by it as advanced 
pupils : only the methods of instruction must vary, according 
to the age and capacity of the pupil." 

Practising upon this theory, our pupils are taught the ele- 
ments of Geometry, at an early age : sometimes, even before 
they commence Arithmetic, or even reading. By means of 

black-board and chalk lines, angles, surfaces and solids, 

triangles, quadrilaterals, circles, and other geometrical figures 
may be taught to a class of very young pupils, in a short 
time. 

I have frequently heard pupils in Mensuration, when asked 
to explain their calculation, answered that they had obtained 
the area of a trapezoid, or rhombus ; but what a trapezoid or 
rhombus is, they could not tell. Sometimes, too, the figure 
was even constructed; but, further than its being the figure in 
the book, they could not tell. The calculation was performed 
by rule, but having no knowledge of what they were calcula- 
ting, it, of course, was not understood. It is unnecessary to 
say, that a pupil, with a knowledge of even the elements of 
Geometry, would not thus work in the dark. 

The remainder of this chapter, will be practical examples 
of the school room. 

When I was a pupil in Algebra, I was taught to work 
Quadratic equations by the following rule in Bonnycastle's 
Algebra. 

" The value of the unknown quantity is always equal to 
half of the coefficient of the second term of the equation, 
taken with a contrary sign together with + the square root 
of the square of this number and the known quantity that 
forms the absolute or third term of the equation." 



96 THE TEACHING OF GEOMETRY AND ALGERRA. 

Of course, I did not understand a word of it.* 

The following is much better. 

"Take half the coefficient of the second term, square it, 
and add the result to both members of the equation. Then 
extract the square root of both members of the equation ; after 
which, transpose the known term to the second member." 

I think, however, both of them useless. 

The following scene lately occurred, in my school room. — 
The pupil had the following equation on his slate. 

x 2 + 8x = 84. 
He was well acquainted with analytical principles ; but this 
equation was something new. What was he to do with the 
8x? He had tried every method, he could think of, before he 
came to me. This was his first complete quadratic equation : 
but as he had been taught to pay no regard to the headings of 
the book — he knew not that he was in a new rule. He ex- 
plained to me his difficulty. 

"Extract the square root of each side of the equation," said 
I, with apparent carelessness. 

" The root of a binomial cannot be obtained," he instantly 
replied. " Suppose you add some number to it to make it an 
even square," I continued, apparently paying but little atten- 
tion to him ; and thinking that his knowledge of the binomial 
theorem would teach him to complete the square. 

But, he seemed lost. 

"I cannot find a number" he continued, "and if I could, it 
would have to be added to the other side also." 

" Well, that could be done; could it not ?" 

" Yes, I suppose it could, by involving the second side." 

" How would it involve the second side ?" 

" By making a binomial of it," was the prompt reply. 

" Are you certain of that?" I asked. 

" Well, I think so," he said, looking intently at the equation. 

" Try it," said I. 

* This can be demonstrated, but what Teacher does it ? 



THE TEACHING OF GEOMETRY AND ALGEBRA. 97 

"I would," he replied, if I could find a number to complete 
the square. 

"Try sixteen," said I. 

It was done, and the square root extracted. 

"Now," said I, "add 16 to the other side." 

It was done. 

" Where is your binomial?" I asked as he stood astonished 
at its simplicity. 

" Where could you find a more beautiful square? and even 
if a sured, you could use decimals." 

" Where did you get the sixteen?" 

"Ay, there's the rub," said I, "had you understood thorough- 
ly the binomial theorem, you would not ask." 

Having now come to the point, where the book begins, it is 
unnecessary to repeat more of the scene. 

I once had a pupil, who having tried in vain for the number 
to complete the square, seemed satisfied with the number I 
gave him, without inquiring how I obtained it. The next 
question presented the same difficulty, and was settled in the 
same manner ; the Teacher finding the required number. 

The next square was completed similarly ; the pupil having 
studied in vain for the number. Had he been able to find the 
number, even by guessing, or by repeated trials, he would 
have been satisfied. He cared not for principle. All he cared 
for was to get the answer: and I resolved to give him a sur- 
feit of guessing. Question after question was tried in vain, 
by the persevering pupil, and as each successive square was 
completed by the Teacher, 

" The more and more his wonder grew," 
how the Teacher obtained the number so quickly ; he still 
thinking that I obtained it, by the same process as he had 
vainly tried. Al length, after having tried nearly every ques- 
tion in the book, he exclaimed disparingly, 

" Mr. Lamborn, how do you find the number so quickly ?" 

" You mean, perhaps," I remarked, "how I obtained it ? for 
you can find it as quickly as I." 



98 THE TEACHING OP GEOMETRY AND ALGEBRA. 

"I can!" he exclaimed in surprise, "how ?" 

" The square of half the coefficient of the second term of 
the first member of the equation, is always the number requir- 
ed," I replied: "which you can obtain as easily, and as quick- 
ly as I can." 

" Why did you not tell me ?" he asked in a reproachful tone. 

" Because," I replied, "you did not ask me." 

Although this answer was not altogether satisfactory to him, 
he needed not to be told again what number would complete 
the square. 

I once took charge of a school, in which was a class in 
Geometry nearly through the book : in the teaching of which 
occurred the following scene : 

One of the pupils has constructed a triangle, whose angles 
are 20, 30, and 40 degrees respectively, taken from the scale 
of chords ; and laid off on the ' chord of sixty? 

" Why did you use the chord of sixty ?"* 

"Because the rule tells me to do so." 

" What is a degree ?" 

No answer. 

" Why did you use sixty degrees ?" I repeated. 

" Because 60 degrees is the radius of a circle." 

" Is 60 degrees the radius of any circle, whether great or 
small ?" 

" No, sir ; the radius of a large circle is greater than that of 
a small one." 

" What is the length of a degree ?" 

" Sixty-nine and a half miles." 

" Is the length of a degree in the circumference of a Grind- 
stone, 69 J miles ?" 

" No, sir." 

" AA r hat then is a degree ?" 

" The 360th part of a circle." 

" Of any circle ? whether large or small ?" 

* The answers were given by different members of the class ; — varying 
in age from twelve to eighteen years. 



THE TEACHING OF GEOMETRY AND ALGEBRA. 99 

" Yes, sir." 

" Has a degree, then, any definite length ? for you know, 
the 360th part of one circle, is much greater than the 
360th part of another circle." The class could proceed no 
farther. They evidently did not understand their subject. — 
The chord of 60 degrees was used in the measurement of 
angles, because the book said it: the same book also telling 
them that 60 degrees was the radius of any circle. 

At length one of the older pupils ,replied: 

" This question has often puzzled me. I am told to take 
60 degrees from the scale, because the radius of every circle, 
whether large or small, measures exactly 60 degrees." 

" Sixty of its own degrees," replied the Teacher, "i. e. sixty 
degrees of the circle which it describes." 

" But," continued the pupil, "the radius which we use from 
the scale of chords, will describe a circumference of but one 
length." 

u Are all scales of chords, alike in length ?" asked the 
Teacher. 

" I suppose so," answered the pupil. 

" Then," continued the Teacher, " all circles must be alike. 
But, as I before told you, a radius of a circle, measures exactly 
60 degrees of that circle, or the 6th part, and therefore has no 
definite length; neither has a degree, which is the 360th part 
of a circle, large or small ; one of the earth's circumference 
being in length about 69 1 miles." 

"But, all the scales we use, are of the same length;" said an- 
other pupil. 

" That is because they are all from the same stamp ; 
but all scales are not alike ; neither does it matter whether 
you take the 60 degrees from a scale at all. The scale is 
merely a convenience. An angle is measured by the arc of 
any circle, whose centre is the point of the angle ; and the 
radius of any circle is sixty degrees. Hence it follows that 
any number of degrees, of the sixty with which an arc is de- 



100 THE TEACHING OF GEOMETRY AND ALGEBSA, 

scribed, measured on that arc, is the measure of the angle.*-- 
Thus 90 degrees of any circle, is a quadrant, measuring aright 
angle ; 45 degrees half a right angle, &c, &c; 60 of the same 
degrees being always the radius of the circle." 

This explanation was accompanied by diagrams. Angles 
of different sizes, were thus demonstrated, until the class un- 
derstood the subject. 

The whole theory of teaching Geometry, with the science 
of measuring, being, as the teaching of Arithmetic, thorough 
explanation, it is unnecessary to prolong this chapter. 

* The difference between the chord of an arc, and its length, should 
be thoronghly explained, as well as the mode of constructing a scale of 
chords. 



CHAPTER VII. 

HOW TO INCREASE YOUR SALARIES. 

Hon. Tho. H. Burrowes, in an address to the Lancaster 
County Educational Association, (October, 1851,) laments the 
want of a " fair compensation to the faithful ' breakers of the 
bread of knowledge' which they so richly deserve." * * * 
"Nor are you, Teachers," he says, "without blame in this 
matter. Your fault has been a want of faithfulness to your- 
selves, and, through yourselves, to the public at large, and to 
the rising generation." 

Bishop Potter, in an address delivered at a meeting of the 
same Association, held in January, 1852, uses the following 
language : " Remember that your best reward comes not from 
your employers. Those who are to give you your most val- 
uable recompense, are not the parents, or directors, of your 
district. They are the little ones. They have been brought 
to you, as the ' little ones' were to Christ that you, too, may 
bless them : and in them, you will find your reward." 

This is true. The Teacher should look for a higher reward, 
than money : but how many of the 10,000 Teachers of Penn- 
sylvania would be satisfied with this reward alone ? They 
demand something more. " The laborer is worthy of his hire." 
It is not to be expected that school Teachers should be more 
self-denying and philanthropic than the " rest of mankind." 
Nor is it right that they should. Those who receive the ben- 
efit of their services should pay for them their equivalent. 

Yet it must be confessed that one great cause of the incom- 
petency of the Teacher's salary is the incompetency of the 
Teacher himself. 



102 HOW TO INCREASE YOUR SALARIES. 

Mr. Page says : " The evil complained of is a mutual one 
* * * so the remedy must be mutual ; the public must be 
enlightened, and Teachers must be improved. But there must 
be also something to warrant the higher rate. We cannot 
expect the people to pay more until they find an article worth 
more." 

You cannot expect people to pay for a thing, until they 
know its worth : and many Teachers are worth no more than 
the small pittance they receive. Their patrons are satisfied 
with their services. They are satisfied with an inferior arti- 
cle, and cannot be expected to pay for a good one, 
without knowing its worth. Let good Teachers make them- 
selves known and valued, and they will be paid. It is true, 
good Teachers are often poorly paid : but in most cases it is 
when their services are not appreciated. His patrons do not 
pay him as a good Teacher, but as a school master : a person 
unfit for any other employment : and before they have had 
time to know his worth — he is off to another district. Again 
he demands a salary in accordance with his worth ; again is 
refused. School masters can be obtained for less, and he is but 
a school master. Can you blame them for not paying more 
than the market price for an article ? Had he remained at his 
former situation another term, he, perhaps, would have made 
his merits known and appreciated. 

If a man wishes to sell a superior article, he must first make 
known its merits. A farmer could not be expected to pay 
$50 for a plow, when he can get one for $20, unless he is 
convinced that the one is worth $30 more than the other : and 
the inventor has no right to complain because the farmer is 
not willing to pay more for the good plow than for the cheap 
one. Neither has the Teacher cause for complaint because 
the school district will not pay for what it does not appreciate. 
Those who appreciate a good article, and who wish to purchase 
it, are willing to pay for it. Those who are satisfied with a 
cheap article, cannot be expected to pay for a good one. 

Fellow Teachers, let us make ourselves known. Already 



HOW TO INCEEASE YOUR SALARIES. 103 

are our services beginning to be known and appreciated. Bu* 
to be known as good Teachers, we must be good Teachers. 
And it is a lamentable fact, that most of the complaints of in- 
competent salary, have been uttered by those who are them- 
selves incompetent. Let us improve ourselves; let us "re- 
spect and honor ourselves, and we will be respected," — and be 
better paid. 

There is now a growing disposition, on the part of the peo- 
ple, to pay the faithful Teacher. The maximum salary is ra- 
pidly increasing throughout the State. And what is the cause 
of the little increase ? The Teacher himself. And " if a 
Teacher fearlessly do that which is right, he may expect to be 
appreciated by the intelligent and liberal portion of the com- 
munity." Let us, then, endeavor by the silent,- steady labors 
of the school room, to cause our patrons to appreciate our 
worth. 

Mr. Page, says : " Talents and attainments must be in ad- 
vance of compensation." 

Mr. Burro wes says: "Many Teachers receive quite as 
much compensation for their services as those services are 
worth. It is the low grade of qualification, that keeps down 
their compensation, more than any other cause ; and it will 
be improved qualification, more also than any other cause, that 
will effect the just remuneration of the Teacher's toil. This 
general law, like all general laws of society, operates justly 
on a large majority of cases, within the sphere of its action. — 
But, like all such laws, it produces hardship in particular 
cases. Thus, while the great mass of ill-qualified, transient 
Teachers are paid quite as much as their defective or careless 
services are worth, the small number of faithful, devoted, self- 
sacrificing, permanent Teachers are rewarded according to the 
same standard, and are therefore deprived of their just rights. 
As inadequate compensation is caused by the number of ill- 
qualified Teachers in the profession, so we shall find it to ad- 
mit of but one remedy — the elevation of the profession in 
qualification." 



104 HOW TO INCREASE YOUR SALARIES. 

This work is begun. Let us continue it, and we will suc- 
ceed. 

" There is a tide in the affairs of men, 
Which, taken at the flood, leads on to fortune." 

Now is that flood in the Teacher's tide. The first field of 
his labor is — his school. The second is — his district, town- 
ship, and county. " The fields are already white to the har- 
vest. And, in the language of a cotemporary, "there never 
was a brighter prospect before us." 

Can you believe that farmers who care so much for the com- 
fort, the convenience, and the health of their horses, their 
oxen, and their cows, do really care less for their children ? 
Certainly not. They are satisfied with an inferior Teacher, 
because they are ignorant. 

De you believe that farmers who spend thousands for the 
comfort, convenience, and health of their horses, would refuse 
or neglect to pay for the comfort, convenience, or health of 
their children ? Did they know that their school houses were 
the abodes of disease, misery and suffering, how long, think 
you, would it be before they would be razed to the ground ? 

Fellow Teachers, do your duty. Qualify yourselves for 
your calling : gain the confidence of your patrons, convince 
them that there is a difference in the quality of the article: and 
you will be paid in accordance with your worth. 

As a last resort, if school directors will not support you, 
stand on your rights. In these days of educational advance- 
ment, a good Teacher is always supported. Start a school of 
vour own ; you will succeed ; and the directors gladly solicit 
vour return. 



CHAPTER vni. 

MISCELLANEOUS. 

For the purpose of making a small book, and not because 
tbe 'Theory and Practice 'of teaching is more than begun, are 
the remaining branches of an English education crowded into 
this chapter. Nor are they less important than those discussed 
in the preceding chapters. If, however, this small work prove 
acceptable to my fellow-teachers, it will be enlarged in a future 
edition. 

Let thorough explanation" be the Teacher's watch-word, 
and all difficulties will disappear. 

Some pupils have a peculiar talent for a particular branch, 
although they may be dull in others. If you succeed in in- 
teresting him in that, (which you surely can.) it is the enter- 
ing wedge to his education. 

In teaching the Natural Sciences, I depend more on oral 
explanation, than on committing to memory, lessons from the 
book. 

I have Cutter's and Lambert's Physiology in my school ; 
but I accomplish more by Cutter's Anatomical Charts — than 
by any book. 

Fifty cents' worth of chemicals will explain the principles 
of Chemistry, better than all the books. 

Natural Philosophy can be explained better by the aid of 
fifty cents' worth of apparatus, than by swallowing 20 books. 

Astronomy, by diagrams on the black-board. 

Botany, by drawing the shape of the leaves, &c, on the 
black-board, with the scientific name of each particular form : 
comparing the leaves themselves with their representations on 
the board: examining flowers, pointing out the stamens, pis- 



106 MISCELLANEOUS. 

tils, corolla, calyx and other parts, explaining their uses, &c. 

True, the advanced pupils should be furnished with books : 
but to put a book into the hands of the novice, except to im- 
prove his reading, is useless. 

So much has been said on the teaching of Drawing, that to 
select even the best, — would make a book. I find the best 
method of teaching children, is by their imitating on the black- 
board. After the pupil has learned to imitate, he advances 
rapidly by any process. Yery young children can soon be 
made to learn to imitate correctly. 

William Eussell says, "Let a large, well-drawn, well- 
colored picture of an animal, or any other object, intelligible 
and interesting to children, be suspended over the black-board : 
let the children be asked a few simple questions about the 
form, color and the habits of the animal, if such is the object 
selected, &c." 

It is hardly necessary to say more on concert exercises, but 
as those who have the most condemned this method of teach- 
ing, admit its uses, so far as I have advocated it, I will quote 
a few lines from Professor Page. He says : 

" It may, sometimes, be useful. A few questions thus an- 
swered, may serve to give animation to a class, when their 
interest begins to flag ; but that which may serve as a stimu- 
lant, must not be relied on for nutrition. As an example of 
its usefulness, I have known a rapid reader tamed into due 
moderation by being put in companionship with others of 
slower speech, just as we tame a friskful colt, by harnessing 
him into a team of grave old horses. But, aside from some such 
definite purpose, I have seen no good cause for this innovation. 
I am satisfied its prevalence is an evil, and worthy of the care- 
ful consideration of Teachers." 

This is one of its principal advantages. In the teaching of 
reading, I have found it of great advantage. If imitation is 
the only true method of teaching reading — (which is generally 
admitted) how can he learn to imitate better than by reading 
in concert with good readers ? As Mr. Page truly says, " he 



MISCELLANEOUS. 107 

will be tamed into moderation ;" he cannot run over the pauses. 
Neither can he lag ; he must keep up with the rest. Nor can 
he read in a different tone, without making discord : which the 
practised ear instantly detects. Great care, however, must be 
observed, or it will produce all those evils described by some 
Teachers. It must be used with discretion : — and more as a 
" stimulant than nutrition." 

Mr. Eussell says, after acknowledging that " much is ap- 
parently done " by chanting tables, &c, &c, says, " but the 
memory, thus cultivated, is verbal, merely ; and the knowledge 
is of words rather than of things." 

Now, if it be right to teach tables at all by memory, then 
is the chanting of them no more " merely verbal, v than any 
other mode. Of the chanting, or concert recitation of any 
thing which exercises more than memory, — Teachers should 
be very careful. 

the teaching of composition. 

We extract a few lines from a description in the Pennsyl- 
vania School Journal, by the compiler, of his mode of teach- 
ing composition. 

First, let the pupil write something upon some subject, no 
matter what, in his own style ; the Teacher correcting the 
orthography and syntax, but not the manner. As the pupil 
advances, let his style be improved. This may be done by 
various methods. One is for the pupil to write on subjects 
made familiar to him by reading and study, such as Grammar, 
Geography, History, &c. His ideas may not be original, nor 
the diction : but he cannot be guilty of gross plagiarism, with- 
out being detected : as the Teacher is as familiar with the 
books, as he is. The ingenuity required, (if nothing more) to 
put the ideas obtained from the book, in other words, will of 
itself improve his style. We sometimes require the pupil to 
read aloud, a portion of history, or any thing else that he can 
understand, and afterwards write it, in his own language, and 
read it aloud to the school. 



108 MISCELLANEOUS. 

Extracts from a report on Composition, read before a meet- 
ing of the State Teachers' Association, held at Pottsville, 
August, 1854 : 

***** ;L et; ^g p U pii s generally read their own 
composition. In large schools, this cannot always be done; 
in such cases let none be read but the best ; and make its being 
read, a reward of excellence. Not merely the best specimens 
of diction, but those containing the smallest number of errors 
in orthography, punctuation, &c., &c, and in the more advanced 
classes, those having the least number of syntactical errors. 
By this means even the dullest cannot fail to acquire, by in- 
dustry and perseverance, the highest distinction in the class- 
When the school is very large, it is necessary to fix the stand- 
ard of excellence high, as time cannot be allowed for the read- 
ing of but a few examples. Let the standard be such that all 
can reach, but let the least error in orthography, the omission 
of the dotting of i, or the crossing of a t, condemn it. 

The productions of one pupil may be sometimes read by an- 
other, who may point out the errors, and correct them, when 
it may be again read, and so continue until all are removed. 

The following from the School Journal strikes us favorably. 
" The pupils sometimes direct their compositions to one of the 
other pupils of the same class, done up in letter form, to be 
read by him. After they are read they are retained by their 
respective readers, until the next composition day, to be cor- 
rected by them, and then read aloud to the school. Sometimes 
they are directed, as amended, to the original authors, to be 
read by them in their corrected form. They are fond of this 
exercise ; and it is astonishing how it increases the demand 

for Dictionaries. We are better at correcting others' faults 
than our own." 

We select the following from the Popular Educator. 

" At first, never mind that the pupil's words are few ; never 
mind that his sentences are ungrammatical ; never mind that 
his thoughts are poor and superficial : let him write something ; 
and let that be his oion." 



MISCELLANEOUS. 109 

Encourage the pupil to use every facility for the improving 
of his style ; but teach him to think, and be original. Com- 
position should be taught, — can be taught, — but merely to 
imitate the style of others, is very nearly allied to plagiarism. 

The design of teaching Composition seems to us to be the 
teaching of thinking beings to express their thoughts clearly,, 
distinctly and grammatically. 

After all, we believe that the best method depends mainly 
on the diligence and the skill of the Teacher. The very worst 
methods may be made effectual for good, by the enthusiastic 
Teacher. If he enter into the feelings of the child, be a child, 
talk like a child, and write as a child, the pupil will improve 
as a child ; and not, as many do, become men in style, while 
they are yet children. 

Extract from an address on Physiology, by Wm. Field, of 
Schuylkill Haven, Pa. : 

" The muscles require rest, after having been vigorously 
exercised : thus we find that a person exercising but one set 
of muscles, soon becomes fatigued ; and this is most strikingly 
illustrated in the school-room. The pupils, by sitting in one 
position for a long time, become restless, uneasy and inatten- 
tive, and thence arises the necessity of frequent recesses : par- 
ticularly for small children. Not that we would have the pu- 
pil spend half of his time upon the play-ground ; but give 
them all the exercise necessary for the health and vigor of 
the body ; and with a healthy robust constitution, what else 
could we expect to find, but an attentive and comprehensive 
mind ? I have met with a few Teachers (and I am happy to 
say, but few) who are opposed to recess, saying that the time 
can be more beneficially employed in the school-room. To 
such we would say — if the want of time is their only excuse, 
give ten minutes recess in the morning and in the afternoon 
session, and they will accomplish more during the day." 

MUSIC. 

" Almost any Teacher can introduce music into his school : 
because, if he cannot sing, he will always find that it will only 



110 MISCELLANEOUS. 

require a little encouragement to induce the scholars to under- 
take to conduct it themselves. It will consume but very lit- 
tle time ; and it is always that time which, if not employed in 
singing, would be otherwise unemployed, or misemployed. — 
It is the united testimony of all who have judiciously intro- 
duced singing into their schools, that it is among the best in- 
strumentalities for the promotion of good feeling and good or- 
der." — Page. 

To teach reading successfully, the Teacher should be well 
acquainted with the elementary sounds of our language, and 
should practise his pupils (especially the younger ones) daily 
on those sounds, in every degree of pitch and force. 

Frequently explode the elementary sounds. The pupils in 
orthography should be taught to spell, not only by the com- 
mon alphabet, but by the phonetic sounds. This will materi- 
ally assist them in acquiring a full, clear, and distinct articu- 
lation. 

Pupils should always stand or sit erect during their recita- 
tions. 

" As soon as a child has learned three words, he should be 
set to read. ' What have you been reading about $ ' is a question 
which must always, without one solitary exception, follow read- 
ing." — George B. Emerson. 

" A Teacher who possesses the ability to read well himself, 
and to infuse the right spirit into his pupils, will form good 
readers." — Charles Northend. 

We close this volume with a few more of the educational 
maxims, selected for the work, many of which its small size 
has excluded : those retained being very minute extracts. 

" The following brief suggestions and rules in relation to 
writing, should be regarded by every Teacher, who would 
produce work of which he need not feel ashamed. 

1st. Require the pupil to sit up while writing. 

2d. Require all turns to be made without raising the pen. 

oth. Insist that the pen be held properly. 



MISCELLANEOUS. Ill 

6th. Only those fingers which hold the pen should move in 
writing. 

7th. The end of the pen-holder should point towards the 
shoulder. 

8th. The hand should not be supported by the wrist, but 
by that part of the arm, a little below the elbow." — Charles 

NORTHEND. 

EXACTNESS IN EXPLANATION. 

" To show what I mean by exactness in explanation, I will 
take a common solution of a single question. — 35 is f of how 
many times 11 ? The pupil says : ' If 85 is I, i- will be $ of 
35 : which is 7 : and § , or the whole will be 7 times 9 ; which is 
63.' Now, the error here, is in saying 7 times 9, instead of 9 
times 7."* — Northend. 

We make this quotation, not to give a particular system of 
analysis, but to enforce the necessity of system in explanation. 
Not to teach the pupil to, parrot like, repeat a certain formula, 
but to explain systematically, clearly, distinctly, and understand- 
ingly. Teachers are apt to pride themselves on some particu- 
lar form, without reflecting that the pupil's own form may be 
as good and even better for him than any other. True, the 
solution should be correct, and explained correctly, and in 
correct language : but let the language (if possible) be the pu- 
pil's own. If it be unsatisfactory, let the Teacher correct it. 
In most cases, if the pupil understands what he is doing, he 
will be right. When he hesitates, blunders, or explains un- 
systematically, and without exactness, it is because he does 
not understand what he is trying to explain. Make it clear to 
his mind, and it will come out. If not, ' draw it out ' by ques- 
tions ; not as the Teacher, given by Mr. Page, drew the 18 
sheep out of the pupil, but an answer of some kind, from which 
to start. If an answer of no kind can be obtained, tell him at 

*This may be illustrated further, thus : — 7 times 9 ninths would be 63 
ninths : or, if one ninth is 7 dollars. 9 ninths would be 9 times 7 dollars ; 
not 7 dollars times 9. Or the price of 130 yards of cloth at 6 dollars a 
yard, is 130 times 6 dollars : not 6 dollars times 130. 



112 MISCELLANEOUS. 

once, and explain it thoroughly, until you are sure that lie un- 
derstands it ; and until he does, — proceed no further. But to 
continue the solution, — 63 are — A of 63 (or 5 ft) times — 11 : 
or as many times 11 as is contained in 63. 

The question may be changed, thus : 

1st. — 63 are 11 times — what number ? 

Ans. — 63 are 11 times A of 63. 

Or — 63 are x times '- of 63. 

X 

2d. — 63 are tV of what number ? 

Ans. — 63 are iV of 11 times 63, &c, &c, &c. 

" Teach the subject rather than the book. Eemember that 
it is not Colburn's arithmetic or Davies' that you are to teach ; 
but arithmetic ; the science of numbers." — George B. Emer- 
son. 

" Make a pupil think that he can do a thing, and he can 
mostly do it." — Northend. 

" Eemember this, — that when the pupil cannot tell, he does 
not know." — Northend. 

"Attention, undivided attention must be required of the 
whole class as long as the recitation continues." — Northend. 

" Let not a Teacher complain too much of the largeness of 
his school. It is physically impossible that a Tencher can 
throw as much energy into his instructions, when they are 
given in the preseuce of but one (or of a very small number) 
as when they are communicated before a large school. The 
efficacy of teaching, depends, very much, upon its vivacity." 
— Bishop Potter. 

" A School Teacher is one who is duly qualified so to culti- 
vate the physical powers, the moral sentiments and the mental 
faculties, as to fit his pupils for the proper discharge of their 
duties. This, and nothing short of it, is the Teacher's true 
office. The time has passed away forever when the Teacher 
was supposed to be a kind of mere conduit -pipe for convey- 
ing, from a given number of books to the memory of the pu- 
pil, the contents of their pages." — Tho. H. Burro wes. 



MISCELLANEOUS. 113 

"The first lesson in Geography might be to set the class to 
draw a map of the school-room." — Emerson. 

" The most effectual way to secure the good will of a scholar 
is to ask him to assist you. Get a turbulent boy to co-operate 
with you in any thing, and you have him? — Emerson. 

" The Teacher's interest in the child will never be without 
its effect upon the parent : and when the parents are friendly 
the pupils are obedient." — Emerson. 

" The Teacher should be cheerful. Cheerfulness in the face 
of a Teacher, is sunshine to the child." — Emerson. 

"Attend Teachers' Institutes, Associations, &c. Visit the 
schools of other Teachers, and witness their modes of teach- 
ing." — NORTHEND. 

" Scientific definitions should be always impressed on the 
mind of the learner by the words of the Teacher, and not by 
or in the words of the book. It must be borne in mind that 
most scientific definitions are made up of words which them- 
selves require explanation to the unlearned ; and that the im- 
pression of these mere words on the memory, adds little to 
the mind's stock of knowledge, without the explanation. — 
Whereas, a preliminary oral explanation, by a judicious 
Teacher, renders every thing clear, and fixes the definition 
and its full significance in the pupil's mind 'indelibly forever. 

In our opinion the properly qualified Teacher is the sole 
head and source of instruction of all kinds in the school ; and 
the school-book is but the representative or exponent of the 
Teacher's knowledge, in the absence of the Teacher." — Tho. 
H. Burrowes. 



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